How do I find the altitude, base and the length of a triangle?

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The base of an Isosceles triangle is $5text cm$ longer than the height. If the area of the triangle is $12text cm^2$. Find the height, base and the length of one of its equal sides.






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    Do you know a formula for the area of a triangle in terms of its base and height? Do you know how to turn sentences into equations?
    – Gerry Myerson
    Oct 13 '15 at 12:34






  • 1




    Let the sides of the triangle be $a, a, 2b$. What can you make of the conditions given?
    – Macavity
    Oct 13 '15 at 12:36















up vote
0
down vote

favorite












The base of an Isosceles triangle is $5text cm$ longer than the height. If the area of the triangle is $12text cm^2$. Find the height, base and the length of one of its equal sides.






triangle







share|cite|improve this question



















  • 3




    Do you know a formula for the area of a triangle in terms of its base and height? Do you know how to turn sentences into equations?
    – Gerry Myerson
    Oct 13 '15 at 12:34






  • 1




    Let the sides of the triangle be $a, a, 2b$. What can you make of the conditions given?
    – Macavity
    Oct 13 '15 at 12:36













up vote
0
down vote

favorite









up vote
0
down vote

favorite











The base of an Isosceles triangle is $5text cm$ longer than the height. If the area of the triangle is $12text cm^2$. Find the height, base and the length of one of its equal sides.






triangle







share|cite|improve this question















The base of an Isosceles triangle is $5text cm$ longer than the height. If the area of the triangle is $12text cm^2$. Find the height, base and the length of one of its equal sides.






triangle




triangle






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edited Oct 13 '15 at 12:48







user249332

















asked Oct 13 '15 at 12:31









Roberto Jacinto

113




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  • 3




    Do you know a formula for the area of a triangle in terms of its base and height? Do you know how to turn sentences into equations?
    – Gerry Myerson
    Oct 13 '15 at 12:34






  • 1




    Let the sides of the triangle be $a, a, 2b$. What can you make of the conditions given?
    – Macavity
    Oct 13 '15 at 12:36













  • 3




    Do you know a formula for the area of a triangle in terms of its base and height? Do you know how to turn sentences into equations?
    – Gerry Myerson
    Oct 13 '15 at 12:34






  • 1




    Let the sides of the triangle be $a, a, 2b$. What can you make of the conditions given?
    – Macavity
    Oct 13 '15 at 12:36








3




3




Do you know a formula for the area of a triangle in terms of its base and height? Do you know how to turn sentences into equations?
– Gerry Myerson
Oct 13 '15 at 12:34




Do you know a formula for the area of a triangle in terms of its base and height? Do you know how to turn sentences into equations?
– Gerry Myerson
Oct 13 '15 at 12:34




1




1




Let the sides of the triangle be $a, a, 2b$. What can you make of the conditions given?
– Macavity
Oct 13 '15 at 12:36





Let the sides of the triangle be $a, a, 2b$. What can you make of the conditions given?
– Macavity
Oct 13 '15 at 12:36











3 Answers
3






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oldest

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0
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Since, the area is given as 12, and area of a triangle is given by $$frac12times textbasetimes textheight=12$$



Now, you are also given that $$textbase=textheight+5$$



So, Use the second information into the formula, generate an equation and solve it!



HINT: $textheight=1 textcm$
$textbase= 6 textcm$






share|cite|improve this answer




















  • I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
    – MonK
    Oct 14 '15 at 13:23










  • I think you are mistaken. Maybe a pen an paper will help :)
    – MonK
    Oct 15 '15 at 11:04










  • Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
    – Emilio Novati
    Oct 15 '15 at 11:29

















up vote
0
down vote













The equation h^2 +5h -24 = 0 is correct. Factoring by inspection: (h+8)(h-3)=0.
The height is 3 cm. bh/2=12, b=8 cm. The isoceles triangle is made of a pair of 3-4-5 ratio right triangles. The equal sides are 10 cm.






share|cite|improve this answer




















  • The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
    – CopyPasteIt
    Jul 1 '17 at 1:32

















up vote
0
down vote













This is a math "word problem". You express the statements mathematically and then use math facts to get a solution.



$B=H+5$



Using the formula for the area of a triangle,



$.5BH=.5(H+5)H=.5(H^2+5H)=12$



Multiplying by 2 we get a quadratic equation,



$h^2 +5h -24 = 0$



Factoring by inspection: $(h+8)(h-3)=0$. The height is 3 cm. and the base is 8 cm.



Since we are dealing with an isosceles triangle, the height can be viewed as the perpendicular bisector of the base. Using Pythagorean's Theorem, you can see that the two equal sides have a length of 5 cm.






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    3 Answers
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    3 Answers
    3






    active

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    active

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    up vote
    0
    down vote













    Since, the area is given as 12, and area of a triangle is given by $$frac12times textbasetimes textheight=12$$



    Now, you are also given that $$textbase=textheight+5$$



    So, Use the second information into the formula, generate an equation and solve it!



    HINT: $textheight=1 textcm$
    $textbase= 6 textcm$






    share|cite|improve this answer




















    • I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
      – MonK
      Oct 14 '15 at 13:23










    • I think you are mistaken. Maybe a pen an paper will help :)
      – MonK
      Oct 15 '15 at 11:04










    • Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
      – Emilio Novati
      Oct 15 '15 at 11:29














    up vote
    0
    down vote













    Since, the area is given as 12, and area of a triangle is given by $$frac12times textbasetimes textheight=12$$



    Now, you are also given that $$textbase=textheight+5$$



    So, Use the second information into the formula, generate an equation and solve it!



    HINT: $textheight=1 textcm$
    $textbase= 6 textcm$






    share|cite|improve this answer




















    • I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
      – MonK
      Oct 14 '15 at 13:23










    • I think you are mistaken. Maybe a pen an paper will help :)
      – MonK
      Oct 15 '15 at 11:04










    • Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
      – Emilio Novati
      Oct 15 '15 at 11:29












    up vote
    0
    down vote










    up vote
    0
    down vote









    Since, the area is given as 12, and area of a triangle is given by $$frac12times textbasetimes textheight=12$$



    Now, you are also given that $$textbase=textheight+5$$



    So, Use the second information into the formula, generate an equation and solve it!



    HINT: $textheight=1 textcm$
    $textbase= 6 textcm$






    share|cite|improve this answer












    Since, the area is given as 12, and area of a triangle is given by $$frac12times textbasetimes textheight=12$$



    Now, you are also given that $$textbase=textheight+5$$



    So, Use the second information into the formula, generate an equation and solve it!



    HINT: $textheight=1 textcm$
    $textbase= 6 textcm$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Oct 13 '15 at 12:54









    MonK

    1,517515




    1,517515











    • I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
      – MonK
      Oct 14 '15 at 13:23










    • I think you are mistaken. Maybe a pen an paper will help :)
      – MonK
      Oct 15 '15 at 11:04










    • Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
      – Emilio Novati
      Oct 15 '15 at 11:29
















    • I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
      – MonK
      Oct 14 '15 at 13:23










    • I think you are mistaken. Maybe a pen an paper will help :)
      – MonK
      Oct 15 '15 at 11:04










    • Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
      – Emilio Novati
      Oct 15 '15 at 11:29















    I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
    – MonK
    Oct 14 '15 at 13:23




    I got the quadratic equation in h as $h^2+5h-24=0$, the solution is 1. What am I missing?
    – MonK
    Oct 14 '15 at 13:23












    I think you are mistaken. Maybe a pen an paper will help :)
    – MonK
    Oct 15 '15 at 11:04




    I think you are mistaken. Maybe a pen an paper will help :)
    – MonK
    Oct 15 '15 at 11:04












    Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
    – Emilio Novati
    Oct 15 '15 at 11:29




    Yes! You are right! I was fixed on a basis shorter than height, not longer as asked from the OP :( ........I deleted all.
    – Emilio Novati
    Oct 15 '15 at 11:29










    up vote
    0
    down vote













    The equation h^2 +5h -24 = 0 is correct. Factoring by inspection: (h+8)(h-3)=0.
    The height is 3 cm. bh/2=12, b=8 cm. The isoceles triangle is made of a pair of 3-4-5 ratio right triangles. The equal sides are 10 cm.






    share|cite|improve this answer




















    • The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
      – CopyPasteIt
      Jul 1 '17 at 1:32














    up vote
    0
    down vote













    The equation h^2 +5h -24 = 0 is correct. Factoring by inspection: (h+8)(h-3)=0.
    The height is 3 cm. bh/2=12, b=8 cm. The isoceles triangle is made of a pair of 3-4-5 ratio right triangles. The equal sides are 10 cm.






    share|cite|improve this answer




















    • The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
      – CopyPasteIt
      Jul 1 '17 at 1:32












    up vote
    0
    down vote










    up vote
    0
    down vote









    The equation h^2 +5h -24 = 0 is correct. Factoring by inspection: (h+8)(h-3)=0.
    The height is 3 cm. bh/2=12, b=8 cm. The isoceles triangle is made of a pair of 3-4-5 ratio right triangles. The equal sides are 10 cm.






    share|cite|improve this answer












    The equation h^2 +5h -24 = 0 is correct. Factoring by inspection: (h+8)(h-3)=0.
    The height is 3 cm. bh/2=12, b=8 cm. The isoceles triangle is made of a pair of 3-4-5 ratio right triangles. The equal sides are 10 cm.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered May 25 '17 at 1:03









    toiler

    2112




    2112











    • The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
      – CopyPasteIt
      Jul 1 '17 at 1:32
















    • The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
      – CopyPasteIt
      Jul 1 '17 at 1:32















    The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
    – CopyPasteIt
    Jul 1 '17 at 1:32




    The equal sides are 5 cm. Since time has passed and no chance of doing someone's homework, I reworked your answer with the details.
    – CopyPasteIt
    Jul 1 '17 at 1:32










    up vote
    0
    down vote













    This is a math "word problem". You express the statements mathematically and then use math facts to get a solution.



    $B=H+5$



    Using the formula for the area of a triangle,



    $.5BH=.5(H+5)H=.5(H^2+5H)=12$



    Multiplying by 2 we get a quadratic equation,



    $h^2 +5h -24 = 0$



    Factoring by inspection: $(h+8)(h-3)=0$. The height is 3 cm. and the base is 8 cm.



    Since we are dealing with an isosceles triangle, the height can be viewed as the perpendicular bisector of the base. Using Pythagorean's Theorem, you can see that the two equal sides have a length of 5 cm.






    share|cite|improve this answer
























      up vote
      0
      down vote













      This is a math "word problem". You express the statements mathematically and then use math facts to get a solution.



      $B=H+5$



      Using the formula for the area of a triangle,



      $.5BH=.5(H+5)H=.5(H^2+5H)=12$



      Multiplying by 2 we get a quadratic equation,



      $h^2 +5h -24 = 0$



      Factoring by inspection: $(h+8)(h-3)=0$. The height is 3 cm. and the base is 8 cm.



      Since we are dealing with an isosceles triangle, the height can be viewed as the perpendicular bisector of the base. Using Pythagorean's Theorem, you can see that the two equal sides have a length of 5 cm.






      share|cite|improve this answer






















        up vote
        0
        down vote










        up vote
        0
        down vote









        This is a math "word problem". You express the statements mathematically and then use math facts to get a solution.



        $B=H+5$



        Using the formula for the area of a triangle,



        $.5BH=.5(H+5)H=.5(H^2+5H)=12$



        Multiplying by 2 we get a quadratic equation,



        $h^2 +5h -24 = 0$



        Factoring by inspection: $(h+8)(h-3)=0$. The height is 3 cm. and the base is 8 cm.



        Since we are dealing with an isosceles triangle, the height can be viewed as the perpendicular bisector of the base. Using Pythagorean's Theorem, you can see that the two equal sides have a length of 5 cm.






        share|cite|improve this answer












        This is a math "word problem". You express the statements mathematically and then use math facts to get a solution.



        $B=H+5$



        Using the formula for the area of a triangle,



        $.5BH=.5(H+5)H=.5(H^2+5H)=12$



        Multiplying by 2 we get a quadratic equation,



        $h^2 +5h -24 = 0$



        Factoring by inspection: $(h+8)(h-3)=0$. The height is 3 cm. and the base is 8 cm.



        Since we are dealing with an isosceles triangle, the height can be viewed as the perpendicular bisector of the base. Using Pythagorean's Theorem, you can see that the two equal sides have a length of 5 cm.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jul 1 '17 at 1:20









        CopyPasteIt

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