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

Answer 1

The line which divides the given triangle into two equal area parts and is parallel to the base of that triangle

creates both a smaller upper triangle which is similar (by angle-angle-angle) to the given triangle and a

trapezoid. The ratio of the area of the upper triangle to that of the given triangle is 1:2.

Therefore, the ratio of the base (the segment we're after here) of the upper triangle to that of the given

triangle is the square root of 1:2 or approximately 0.707. So, the segment length is 26x0.707, or about

18.4.

Note that if the original parallel line to the base had past through the midpoints of both legs, it would have

created a mid-segment, whose length would have been one-half of 26 or 13 units. The area of the smaller

upper triangle would, then, be one-fourth of the area of the given triangle.

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