Two isosceles triangles have their corresponding angles equal and… - Vidyadip

MCQ

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
$36 : 25$
✓
$5 : 6$
D
$6 : 5$

✓

Answer

Correct option: C.

$5 : 6$

Since the triangles have correspondin angles equal, the triangles are similar.
Let the areas of the triangles be $\mathrm{A}_1$ and $\mathrm{A}_2$,
and let their corresponding heights be $\mathrm{h}_1$ and $\mathrm{h}_2$,
$\frac{\text{ar}(\text{A}_1)}{\text{ar}(\text{A}_2)}=\frac{\text{h}_1^2}{\text{h}_2^2}$
$\Rightarrow\frac{25}{36}=\frac{\text{h}_1^2}{\text{h}_2^2}$
$\Rightarrow\frac{\text{h}_1}{\text{h}_2}=\frac{5}{6}$
So, the ratio of their heights is $5 : 6$.

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