A B C is such that A B=3 cm, B C=2 cm, C A=2.5 cm. If A B C D E F… - Vidyadip

MCQ

$\triangle A B C$ is such that $A B=3 cm, B C=2 cm, C A=2.5 cm$. If $\triangle A B C \sim \triangle D E F$ and $E F=4 cm$, then perimeter of $\triangle D E F$ is

A
7.5 cm
✓
15 cm
C
22.5 cm
D
30 cm

✓

Answer

Correct option: B.

15 cm

(B)15
It is given that
$\begin{array}{l}\Delta A B C \sim \triangle D E F \\ \Rightarrow \quad \frac{A B}{D E}=\frac{B C}{E F}=\frac{A C}{D F}=\frac{A B+B C+C A}{D E+E F+D F} \\ \Rightarrow \quad \frac{B C}{F E}=\frac{3+2+2.5}{\text { Perimeter of } \triangle D E F} \Rightarrow \frac{4}{2}=\frac{7.5}{\text { Perimeter of } \triangle D E F} \Rightarrow \text { Perimeter of } \triangle D E F=15 cm .\end{array}$

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