such that ar( )=36 cm^2 and ar( )=49 cm^2. Then, the ratio of the… - Vidyadip

MCQ

$\Rightarrow\triangle\text{ABC}\sim\triangle\text{DEF}$ such that $\text{ar}(\triangle\text{ABC})=36\text{ cm}^2$ and $\text{ar}(\triangle\text{DEF})=49\text{ cm}^2.$ Then, the ratio of their corresponding sides is :

A
$36 : 49$
✓
$6 : 7$
C
$7 : 6$
D
$\sqrt{6}:\sqrt{7}$

✓

Answer

Correct option: B.

$6 : 7$

$\Rightarrow\triangle\text{ABC}\sim\triangle\text{DEF}$
$\Rightarrow\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{DEF})}=\frac{\text{AB}^2}{\text{DE}^2}$
$\Rightarrow\frac{36}{49}=\frac{\text{AB}^2}{\text{DE}^2}$
$\Rightarrow\frac{\text{AB}}{\text{DE}}=\frac{6}{7}$
Since the triangle are similar,
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=\frac{6}{7}$
So, the ratio is $6 : 7.$

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