Ava is solving a geometry problem. The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two equal area parts. She solved for the length of the segment dividing the triangle and got 25.455. How did Ava get that answer?

The ratio of areas of similar triangles is the square of the ratio of their linear dimensions. If the smaller triangle is 1/2 the area of the larger, then its linear dimensions are √ (1/2) those of the larger triangle.

smaller side length = √ (1/2) * larger side length

= (√2) / 2*36 = 18√2 ≈ 25.4558