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 $A_1$ and $A_2,$
and let their corresponding heights be $h_1$ and $h_2,$
$\frac{\text{ar}(\text{A}_1)}{\text{ar}(\text{A}_2)}=\frac{\text{h}_1^2}{\text{h}_2^2}$
$\Rightarrow\frac{25}{36}=\frac{\text{h}_1^2}{\text{h}_2^2}$
$\Rightarrow\frac{\text{h}_1}{\text{h}_2}=\frac{5}{6}$
So, the ratio of their heights is $5 : 6.$
Let the areas of the triangles be $A_1$ and $A_2,$
and let their corresponding heights be $h_1$ and $h_2,$
$\frac{\text{ar}(\text{A}_1)}{\text{ar}(\text{A}_2)}=\frac{\text{h}_1^2}{\text{h}_2^2}$
$\Rightarrow\frac{25}{36}=\frac{\text{h}_1^2}{\text{h}_2^2}$
$\Rightarrow\frac{\text{h}_1}{\text{h}_2}=\frac{5}{6}$
So, the ratio of their heights is $5 : 6.$
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