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.

Step-by-step explanation:

It is given that the length of triangle base is 26, then let ABC  be the triangle and BC be the base of the triangle=26.Let DE be the parallel line to the base that divides triangle ABC into two equal area parts.

Now, Let AD=a, DB=b, DE=c, AE=d and EC=e, then

Since,  triangle ABC is similar to triangle ADE, thus using basic proportions, we get

Taking the first two equalities,we get

Thus, the length of the segment between triangle legs is