# Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25 : 36.

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

Solution:

(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,

$\frac{\operatorname{ar}\left(\triangle_{1}\right)}{\operatorname{ar}\left(\triangle_{2}\right)}=\frac{25}{36}=\frac{x^{2}}{y^{2}}$

$\Rightarrow \frac{x^{2}}{y^{2}}=\frac{25}{36}$

$\Rightarrow \frac{x}{y}=\sqrt{\frac{25}{36}}=\frac{5}{6}=5: 6$