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

Answer: 18 root 2

Explanation:

Answer 2

18√2

Explanation:

The smaller triangle resulting from the division is similar to the original. Since its area is a factor of 1/2 relative to the larger triangle area, its linear dimensions must be a factor of √(1/2) = (√2)/2 times those of the larger triangle. Then the parallel base will have a length of ...

36·(√2)/2 = 18√2