What is minimum value of $l$ where $l$ is one of the prependiculer line of triangle

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$l,k,2$ are length of prependicular line of triangle$ABC$.Where $frack+2k-2$ is not integer ,but rational number, Integer $l$'s maximum value is $f(k)$, find $f(k)$



I didn't have an idea to solve this problem. Please give some hint...







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  • I would always start something like this by drawing and labelling a diagram.
    – Bruce
    Aug 22 at 11:07










  • @Bruce I'm sorry about I can't draw some diagram in tax..... I can't imagine condition $frack+2k-2$
    – user366725
    Aug 22 at 11:10










  • Try first to define what exactly you mean by "perpendicular line of triangle"...Do you mean heights of the triangle? Perpendicular bisectors of the sides and their length to their common point? I really can't understand that.
    – DonAntonio
    Aug 22 at 11:16










  • @DonAntonio yes,It's three hight of triangle
    – user366725
    Aug 22 at 11:19










  • @user366725 Good...then I only don't understand the rest: The three heights of a triangle have lengths $;l,,k,,2;$ , right? You're given $;frack+2k-2;$ is a rational number. Then you say, I think, that the maximum value $;l;$ can attain is $;f(k);$ , which I suppose means a number depending only on $;k;$ ...Yep, I've no idea what to do. Perhaps some diagram would help.There are sites that help you with this, and then you can glue the diagram here.
    – DonAntonio
    Aug 22 at 11:49















up vote
0
down vote

favorite












$l,k,2$ are length of prependicular line of triangle$ABC$.Where $frack+2k-2$ is not integer ,but rational number, Integer $l$'s maximum value is $f(k)$, find $f(k)$



I didn't have an idea to solve this problem. Please give some hint...







share|cite|improve this question






















  • I would always start something like this by drawing and labelling a diagram.
    – Bruce
    Aug 22 at 11:07










  • @Bruce I'm sorry about I can't draw some diagram in tax..... I can't imagine condition $frack+2k-2$
    – user366725
    Aug 22 at 11:10










  • Try first to define what exactly you mean by "perpendicular line of triangle"...Do you mean heights of the triangle? Perpendicular bisectors of the sides and their length to their common point? I really can't understand that.
    – DonAntonio
    Aug 22 at 11:16










  • @DonAntonio yes,It's three hight of triangle
    – user366725
    Aug 22 at 11:19










  • @user366725 Good...then I only don't understand the rest: The three heights of a triangle have lengths $;l,,k,,2;$ , right? You're given $;frack+2k-2;$ is a rational number. Then you say, I think, that the maximum value $;l;$ can attain is $;f(k);$ , which I suppose means a number depending only on $;k;$ ...Yep, I've no idea what to do. Perhaps some diagram would help.There are sites that help you with this, and then you can glue the diagram here.
    – DonAntonio
    Aug 22 at 11:49













up vote
0
down vote

favorite









up vote
0
down vote

favorite











$l,k,2$ are length of prependicular line of triangle$ABC$.Where $frack+2k-2$ is not integer ,but rational number, Integer $l$'s maximum value is $f(k)$, find $f(k)$



I didn't have an idea to solve this problem. Please give some hint...







share|cite|improve this question














$l,k,2$ are length of prependicular line of triangle$ABC$.Where $frack+2k-2$ is not integer ,but rational number, Integer $l$'s maximum value is $f(k)$, find $f(k)$



I didn't have an idea to solve this problem. Please give some hint...









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 22 at 22:44

























asked Aug 22 at 11:04









user366725

587




587











  • I would always start something like this by drawing and labelling a diagram.
    – Bruce
    Aug 22 at 11:07










  • @Bruce I'm sorry about I can't draw some diagram in tax..... I can't imagine condition $frack+2k-2$
    – user366725
    Aug 22 at 11:10










  • Try first to define what exactly you mean by "perpendicular line of triangle"...Do you mean heights of the triangle? Perpendicular bisectors of the sides and their length to their common point? I really can't understand that.
    – DonAntonio
    Aug 22 at 11:16










  • @DonAntonio yes,It's three hight of triangle
    – user366725
    Aug 22 at 11:19










  • @user366725 Good...then I only don't understand the rest: The three heights of a triangle have lengths $;l,,k,,2;$ , right? You're given $;frack+2k-2;$ is a rational number. Then you say, I think, that the maximum value $;l;$ can attain is $;f(k);$ , which I suppose means a number depending only on $;k;$ ...Yep, I've no idea what to do. Perhaps some diagram would help.There are sites that help you with this, and then you can glue the diagram here.
    – DonAntonio
    Aug 22 at 11:49

















  • I would always start something like this by drawing and labelling a diagram.
    – Bruce
    Aug 22 at 11:07










  • @Bruce I'm sorry about I can't draw some diagram in tax..... I can't imagine condition $frack+2k-2$
    – user366725
    Aug 22 at 11:10










  • Try first to define what exactly you mean by "perpendicular line of triangle"...Do you mean heights of the triangle? Perpendicular bisectors of the sides and their length to their common point? I really can't understand that.
    – DonAntonio
    Aug 22 at 11:16










  • @DonAntonio yes,It's three hight of triangle
    – user366725
    Aug 22 at 11:19










  • @user366725 Good...then I only don't understand the rest: The three heights of a triangle have lengths $;l,,k,,2;$ , right? You're given $;frack+2k-2;$ is a rational number. Then you say, I think, that the maximum value $;l;$ can attain is $;f(k);$ , which I suppose means a number depending only on $;k;$ ...Yep, I've no idea what to do. Perhaps some diagram would help.There are sites that help you with this, and then you can glue the diagram here.
    – DonAntonio
    Aug 22 at 11:49
















I would always start something like this by drawing and labelling a diagram.
– Bruce
Aug 22 at 11:07




I would always start something like this by drawing and labelling a diagram.
– Bruce
Aug 22 at 11:07












@Bruce I'm sorry about I can't draw some diagram in tax..... I can't imagine condition $frack+2k-2$
– user366725
Aug 22 at 11:10




@Bruce I'm sorry about I can't draw some diagram in tax..... I can't imagine condition $frack+2k-2$
– user366725
Aug 22 at 11:10












Try first to define what exactly you mean by "perpendicular line of triangle"...Do you mean heights of the triangle? Perpendicular bisectors of the sides and their length to their common point? I really can't understand that.
– DonAntonio
Aug 22 at 11:16




Try first to define what exactly you mean by "perpendicular line of triangle"...Do you mean heights of the triangle? Perpendicular bisectors of the sides and their length to their common point? I really can't understand that.
– DonAntonio
Aug 22 at 11:16












@DonAntonio yes,It's three hight of triangle
– user366725
Aug 22 at 11:19




@DonAntonio yes,It's three hight of triangle
– user366725
Aug 22 at 11:19












@user366725 Good...then I only don't understand the rest: The three heights of a triangle have lengths $;l,,k,,2;$ , right? You're given $;frack+2k-2;$ is a rational number. Then you say, I think, that the maximum value $;l;$ can attain is $;f(k);$ , which I suppose means a number depending only on $;k;$ ...Yep, I've no idea what to do. Perhaps some diagram would help.There are sites that help you with this, and then you can glue the diagram here.
– DonAntonio
Aug 22 at 11:49





@user366725 Good...then I only don't understand the rest: The three heights of a triangle have lengths $;l,,k,,2;$ , right? You're given $;frack+2k-2;$ is a rational number. Then you say, I think, that the maximum value $;l;$ can attain is $;f(k);$ , which I suppose means a number depending only on $;k;$ ...Yep, I've no idea what to do. Perhaps some diagram would help.There are sites that help you with this, and then you can glue the diagram here.
– DonAntonio
Aug 22 at 11:49











1 Answer
1






active

oldest

votes

















up vote
0
down vote



accepted










First, we set the Area of the triangle be “lkt”. Then the three sides of the triangle are 2kt, 2lt, and lkt. So, we have 2k+2l>lk, 2k+lk>2l, and 2l+lk>2k. To these, we have 2k>l(k-2), 2k>l(2-k), and (2+k)l>2k. if k is more than 2, l is less than 2k/(k-2). If k is less than 2, l is less than 2k/(2-k). if k is 2, l just needs to be more than 1.






share|cite|improve this answer




















  • if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
    – Xinye Bao
    Aug 22 at 20:04










  • I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
    – user366725
    Aug 22 at 22:17






  • 1




    I'm sorry but would you explain more specifically?? I can't understand....TT
    – user366725
    Aug 24 at 16:02










  • I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
    – Xinye Bao
    Aug 26 at 14:23










  • Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
    – user366725
    Aug 26 at 14:26










Your Answer




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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote



accepted










First, we set the Area of the triangle be “lkt”. Then the three sides of the triangle are 2kt, 2lt, and lkt. So, we have 2k+2l>lk, 2k+lk>2l, and 2l+lk>2k. To these, we have 2k>l(k-2), 2k>l(2-k), and (2+k)l>2k. if k is more than 2, l is less than 2k/(k-2). If k is less than 2, l is less than 2k/(2-k). if k is 2, l just needs to be more than 1.






share|cite|improve this answer




















  • if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
    – Xinye Bao
    Aug 22 at 20:04










  • I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
    – user366725
    Aug 22 at 22:17






  • 1




    I'm sorry but would you explain more specifically?? I can't understand....TT
    – user366725
    Aug 24 at 16:02










  • I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
    – Xinye Bao
    Aug 26 at 14:23










  • Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
    – user366725
    Aug 26 at 14:26














up vote
0
down vote



accepted










First, we set the Area of the triangle be “lkt”. Then the three sides of the triangle are 2kt, 2lt, and lkt. So, we have 2k+2l>lk, 2k+lk>2l, and 2l+lk>2k. To these, we have 2k>l(k-2), 2k>l(2-k), and (2+k)l>2k. if k is more than 2, l is less than 2k/(k-2). If k is less than 2, l is less than 2k/(2-k). if k is 2, l just needs to be more than 1.






share|cite|improve this answer




















  • if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
    – Xinye Bao
    Aug 22 at 20:04










  • I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
    – user366725
    Aug 22 at 22:17






  • 1




    I'm sorry but would you explain more specifically?? I can't understand....TT
    – user366725
    Aug 24 at 16:02










  • I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
    – Xinye Bao
    Aug 26 at 14:23










  • Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
    – user366725
    Aug 26 at 14:26












up vote
0
down vote



accepted







up vote
0
down vote



accepted






First, we set the Area of the triangle be “lkt”. Then the three sides of the triangle are 2kt, 2lt, and lkt. So, we have 2k+2l>lk, 2k+lk>2l, and 2l+lk>2k. To these, we have 2k>l(k-2), 2k>l(2-k), and (2+k)l>2k. if k is more than 2, l is less than 2k/(k-2). If k is less than 2, l is less than 2k/(2-k). if k is 2, l just needs to be more than 1.






share|cite|improve this answer












First, we set the Area of the triangle be “lkt”. Then the three sides of the triangle are 2kt, 2lt, and lkt. So, we have 2k+2l>lk, 2k+lk>2l, and 2l+lk>2k. To these, we have 2k>l(k-2), 2k>l(2-k), and (2+k)l>2k. if k is more than 2, l is less than 2k/(k-2). If k is less than 2, l is less than 2k/(2-k). if k is 2, l just needs to be more than 1.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 22 at 20:03









Xinye Bao

363




363











  • if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
    – Xinye Bao
    Aug 22 at 20:04










  • I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
    – user366725
    Aug 22 at 22:17






  • 1




    I'm sorry but would you explain more specifically?? I can't understand....TT
    – user366725
    Aug 24 at 16:02










  • I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
    – Xinye Bao
    Aug 26 at 14:23










  • Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
    – user366725
    Aug 26 at 14:26
















  • if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
    – Xinye Bao
    Aug 22 at 20:04










  • I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
    – user366725
    Aug 22 at 22:17






  • 1




    I'm sorry but would you explain more specifically?? I can't understand....TT
    – user366725
    Aug 24 at 16:02










  • I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
    – Xinye Bao
    Aug 26 at 14:23










  • Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
    – user366725
    Aug 26 at 14:26















if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
– Xinye Bao
Aug 22 at 20:04




if there are mistakes, I will revise the answer. and I do not know why (k+2)/(k-2) is post.
– Xinye Bao
Aug 22 at 20:04












I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
– user366725
Aug 22 at 22:17




I'm sorry about that I didn't write correctly. frack+2k-2 is rational number that is not integer. For example when k=3,5/1=5 So k=/=3
– user366725
Aug 22 at 22:17




1




1




I'm sorry but would you explain more specifically?? I can't understand....TT
– user366725
Aug 24 at 16:02




I'm sorry but would you explain more specifically?? I can't understand....TT
– user366725
Aug 24 at 16:02












I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
– Xinye Bao
Aug 26 at 14:23




I mean the item about the rational number does not have any meaning in my opinion. It may just show that k is a rational number since (k+2)/(k-2)=1+4/(k-2)
– Xinye Bao
Aug 26 at 14:23












Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
– user366725
Aug 26 at 14:26




Thank you to explain about that,but I didn't understand your answer........ what means Area is lkt?
– user366725
Aug 26 at 14:26












 

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