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?

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.