Question

Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25 : 36. The ratio of their corresponding heights is
(a) 25 : 36
(b) 36 : 25
(c) 5 : 6
(d) 6 : 5

Answer 1

(c) 5:6
Let x and y be the corresponding heights of the two triangles.
It is given that the corresponding angles of the triangles are equal.
Therefore, the triangles are similar. (By AA criterion)
Hence,
$$\begin{gathered} \frac{ar\left({△}_1\right)}{ar\left({△}_2\right)}=\frac{25}{36}=\frac{x^2}{y^2} \\ \Rightarrow \frac{x^2}{y^2}=\frac{25}{36} \\ \Rightarrow \frac{x}{y}=\sqrt{\frac{25}{36}}=\frac{5}{6}=5:6 \end{gathered}$$