Question

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle

Answer 1

18√2

Explanation:

The area of the smaller triangle is 1/2 that of the larger one. Since the triangles are similar, the dimensions of the smaller triangle are √(1/2) those of the larger one.

36 · √(1/2) = 36 · (√2)/2 = 18√2 . . . . length of line dividing the triangle