Similarity on trinagles and trapezoids

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

For the ratio of the areas to be 1 / 2 the ratio of the linear measures must be 1 / √2.

There x / 36 = 1 / √2, x = 36 / √2, x = 18√2.