Question

Two isosceles triangles have equal vertical angles and their areas are in the ratio 36 :25 Find the ratio of their corresponding heights.

Answer 1

The areas of two similar, are in the ratio of the squares of the corresponding attitudes.

$\therefore \frac{ar\left(\Delta ABC\right)}{ar\left(\Delta DEF\right)}=\frac{A{P}^2}{D{Q}^2}$

$\therefore \frac{36}{25}=\frac{A{P}^2}{D{Q}^2}$

$\therefore \frac{AP}{DQ}=\frac{6}{5}$.