Question

The length of triangle base is 26. A line, which is parallel to the base divides the triangle into two equal area parts. Find the length of the segment between triangle legs.

Answer 1

13√2

Explanation:

The parallel segment creates a similar triangle with half the area of the larger one. When the areas of the triangles have ratio 1/2, the linear dimensions of the triangles have a ratio that is the square root of that: √(1/2) = (√2)/2. Thus, the segment length is ...

26 · (√2)/2 = 13√2