SOLUTION: The area of a triangle with base 24 cm is trisected by two segments parallel to the base. What is the length of the longer of these segments?

Question 1107310: The area of a triangle with base 24 cm is trisected by two segments parallel to the base. What is the length of the longer of these segments?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Since the area of the original triangle was trisected, you have


    - the smallest triangle of the area of , where S is the area of the original triangle,  and

    - the middle triangle with the area of .


The three triangles are similar.  The ratio of the areas of the middle to the original is .


Hence, the ratio of their linear elements is  .


It means that the length under the question is    cm.

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