In and , we have AB DE = BC EF = AC DF =5 7 , then ar( ):ar( )=? - Vidyadip

MCQ

In $\triangle\text{ABC}$ and $\triangle\text{DEF},$ we have $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=\frac{5}{7},$ then $\text{ar}(\triangle\text{ABC}):\text{ar}(\triangle\text{DEF})=?$

A
$5 : 7$
✓
$25 : 49$
C
$49 : 25$
D
$125 : 343$

✓

Answer

Correct option: B.

$25 : 49$

In $\triangle\text{ABC}$ and $\triangle\text{DEF},$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=\frac{5}{7}$
$\Rightarrow\triangle\text{ABC}\sim\triangle\text{DEF} ....(\text{SSS}$ criterion for Similarity$)$
$\Rightarrow\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{DEF})}=\frac{\text{AB}^2}{\text{DE}^2}=\frac{5^2}{7^2}=\frac{25}{49}$
So, the ratio is $25 : 49.$

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