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

25 : 35

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36 : 25

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5 : 6

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6 : 5

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Solution

The correct option is C $5 : 6$
We know, ratios of areas of similar triangles is equal to ratio of squares of their corresponding sides.
Hence,

$\frac{A r e a o f △_{1}}{A r e a o f △_{2}} = \frac{(h e i g h t o f △_{1})^{2}}{(h e i g h t o f △_{2})^{2}}$

Taking square root on both sides,

$\frac{(h e i g h t o f △_{1})}{(h e i g h t o f △_{2})} = \sqrt{\frac{A r e a o f △_{1}}{A r e a o f △_{2}}}$

$\frac{(h e i g h t o f △_{1})}{(h e i g h t o f △_{2})} = \sqrt{\frac{25}{36}} = \frac{5}{6}$

Option C

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r Two Isosceles triangles have equal vertical angles and their areas are in the ratio 36:25 find then ratio of their corresponding height.

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