Question 1101147
<br>Let the triangle be ABC, with base BC.  Let the longest segment parallel to BC inside the triangle be DE.<br>
The area of triangle ADE is 4/5 the area of triangle ABC; and the triangles are similar.<br>
If the ratio of the areas of the two triangles is 4:5, the ratio of similar lengths in the two triangles is sqrt(4):sqrt(5).<br>
So the length of DE is {{{20 * (sqrt(4)/sqrt(5)) = 40/sqrt(5) = 8*sqrt(5)}}}