such that ar( )=36cm^2 and ar( )=49cm^2. Then, the ratio of their corresponding sides is:

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

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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