Could someone please help me with this question from a MAOL math competition Matemaattisten Aineiden Opettajien Liitto MAOL ry : Lukion matematiikka ?

We have a triangle. The height of the triangle divides the base of the triangle into two parts, which are 14 cm and 36 cm. Another line parallel to the height is drawn. This line divides the triangle into two equal ( in terms of area) parts. How long are the segments into which this line divides the base of the triangle?

The ratios of the segment of bases and the areas are related so

$\displaystyle \frac{\frac{1}{2}ABC}{\frac{18}{25}ABC}=\frac{25}{ 36}=(\frac{AE}{AD})^2=\frac{{AE}^2}{36^2}$

Then the sample answer says something weird. Is there any reason we would raise the ratio of two segments to the power of two?

Thank you!