SOLUTION: The area of a triangle is divided into 6 equal parts by line segments parallel to one side. If the length of that side is 24cm, find the length of the longer of the line segments.
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-> SOLUTION: The area of a triangle is divided into 6 equal parts by line segments parallel to one side. If the length of that side is 24cm, find the length of the longer of the line segments.
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Question 1149586: The area of a triangle is divided into 6 equal parts by line segments parallel to one side. If the length of that side is 24cm, find the length of the longer of the line segments. Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
Each of the line segments parallel to one side of the triangle, along with portions of the other two sides, forms a triangle that is similar to the whole triangle.
The triangle formed by the longest of those parallel line segments has an area 5/6 of the area of the original. That is, the ratio of the areas is 5:6.
In any two similar figures, if the ratio of the areas is A:B, then the ratio of similarity is sqrt(A):sqrt(B). So in this problem the ratio of similarity is sqrt(5):sqrt(6).
And so the length of the longest of the line segments parallel to the side with length 24 is
