A triangle with three cevians

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The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?




enter image description here



I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.



I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.



Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.



How can I solve this?







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    up vote
    0
    down vote

    favorite













    The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?




    enter image description here



    I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.



    I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.



    Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.



    How can I solve this?







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite












      The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?




      enter image description here



      I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.



      I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.



      Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.



      How can I solve this?







      share|cite|improve this question















      The figure to the right shows a triangle with three cevians drawn through an interior point, and all perimeter segment lengths are given in meters. What is the value of s?




      enter image description here



      I'm not sure if there is any significance in all three ceva meeting at one point within the triangle... I feel like there might be, but I don't see how to utilise this fact.



      I thought using heron's formula and then comparing it to another way of getting the triangle's area. However, I'm not sure how I can get the triangle's area the second (unknown) way.



      Perhaps I could use triangle inequality, but that doesn't seem to get me very far, either.



      How can I solve this?









      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 26 at 13:34









      greedoid

      27.9k93776




      27.9k93776










      asked Aug 26 at 13:10









      jjhh

      2,0291918




      2,0291918




















          1 Answer
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          up vote
          2
          down vote



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          Do you know Ceva's theorem? Acording to that theorem we have:



          $$sover 5cdot 4over 3cdot 4over 2=1$$



          so...






          share|cite|improve this 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
            2
            down vote



            accepted










            Do you know Ceva's theorem? Acording to that theorem we have:



            $$sover 5cdot 4over 3cdot 4over 2=1$$



            so...






            share|cite|improve this answer
























              up vote
              2
              down vote



              accepted










              Do you know Ceva's theorem? Acording to that theorem we have:



              $$sover 5cdot 4over 3cdot 4over 2=1$$



              so...






              share|cite|improve this answer






















                up vote
                2
                down vote



                accepted







                up vote
                2
                down vote



                accepted






                Do you know Ceva's theorem? Acording to that theorem we have:



                $$sover 5cdot 4over 3cdot 4over 2=1$$



                so...






                share|cite|improve this answer












                Do you know Ceva's theorem? Acording to that theorem we have:



                $$sover 5cdot 4over 3cdot 4over 2=1$$



                so...







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Aug 26 at 13:33









                greedoid

                27.9k93776




                27.9k93776



























                     

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