In ABC, it is given that A B=9 cm, BC=6 cm and C A=7.5 cm. Also, … - Vidyadip

MCQ

In $\triangle \text{ABC}$, it is given that $A B=9 \ cm$, $BC=6 \ cm$ and $C A=7.5 \ cm$. Also, $\triangle \text{DEF}$ is given such that $\text{EF}=8 \ cm$ and $\triangle \text{DEF} \sim \triangle \text{ABC}$. Then, perimeter of $\triangle \text{DEF}$ is

A
$22.5 \ cm$
B
$25 \ cm$
C
$27 \ cm$
✓
$30 \ cm$

✓

Answer

Correct option: D.

$30 \ cm$

Perimeter of
$\triangle \text{ABC} =(9+6+7.5) \ cm$
$ =22.5 \ cm$
Let the perimeter of $\triangle \text{DEF}$ be $p \ cm$.
Given $\triangle \text{DEF} \sim \triangle \text{ABC}$
$\Rightarrow \frac{\text { Perimeter of } \triangle DEF}{\text { Perimeter of } \triangle A B C}=\frac{E F}{B C}$
$\Rightarrow \frac{p}{22.5}=\frac{8}{6}$
$\Rightarrow p=\frac{22.5 \times 8}{6}$
$=\frac{225 \times 8}{60}$
$=30 \ cm$

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