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

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Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25 : 36. The ratio of their corresponding heights is 5 : 6. Explanation: The two triangles have corresponding angles equal and so they are similar. $\therefore$ The ratio of their areas is equal to the ratio of the squares of their corresponding sides, but the ratio of their corresponding sides is equal to the ratio of their corresponding altitudes or heights. So, the ratio of their areas is equal to the ratio of the squares of their heights. Now, ratio of their areas = $\frac{25}{36}$ = 5^$\frac{2}{6}$^2 $\Rightarrow$ Ratio of their heights = $\frac{5}{6}$.

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