In , it is given that AB = 9 cm, BC = 6 cm and CA = 7.5 cm. Also,… - Vidyadip

MCQ

In $\triangle\text{ABC},$ it is given that $AB = 9\ cm, BC = 6\ cm$ and $CA = 7.5\ cm$. Also, $\triangle\text{DEF}$ is given such that $EF = 8\ cm$ and $\triangle\text{DEF}\sim\triangle\text{ABC}.$ Then, perimeter of $\triangle\text{DEF}$ 1s:

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

✓

Answer

Correct option: D.

$30\ cm$

$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\Rightarrow\frac{\text{Perimeters of }\triangle\text{DEF}}{\text{Perimeters of }\triangle\text{ABC}}=\frac{\text{EF}}{\text{BC}}$
$\Rightarrow\frac{\text{Perimeters of }\triangle\text{DEF}}{\text{AB+BC+AC}}=\frac{8}{6}$
$\Rightarrow\frac{\text{Perimeters of }\triangle\text{DEF}}{9+6+7.5}=\frac{8}{6}$
$\Rightarrow\frac{\text{Perimeters of }\triangle\text{DEF}}{22.5}=\frac{4}{3}$
$\Rightarrow\text{Perimeters of }\triangle\text{DEF}=\frac{4\times22.5}{3}$
$\Rightarrow\text{Perimeters of }\triangle\text{DEF}=30\text{cm}$

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