SOLUTION: The area of a triangle is divided into 5 equal parts by line segments parallel to one side. If the length of that side is 20 cm, find the length of the longest line segment inside

Question 1101147: The area of a triangle is divided into 5 equal parts by line segments parallel to one side. If the length of that side is 20 cm, find the length of the longest line segment inside the triangle, in cm.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let the triangle be ABC, with base BC. Let the longest segment parallel to BC inside the triangle be DE.

The area of triangle ADE is 4/5 the area of triangle ABC; and the triangles are similar.

If the ratio of the areas of the two triangles is 4:5, the ratio of similar lengths in the two triangles is sqrt(4):sqrt(5).

So the length of DE is

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