$△$ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$ DEF is similar to $△$ ABC. If EF = 4 cm, then the perimeter of $△$ DEF is

7.5 cm

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15 cm

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22.5 cm

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30 cm

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Solution

The correct option is B
15 cm

Given that $Δ A B C \sim Δ D E F$
and AB = 3 cm, BC = 2 cm and CA = 2.5 cm, EF = 4 cm.

$∴ \frac{A B}{D E} = \frac{A C}{D F} = \frac{B C}{E F} ∵ Δ A B C \sim Δ D E F$

$⟹ \frac{B C}{E F} = \frac{2}{4} = \frac{1}{2}$

$⟹$ Corresponding sides of $Δ D E F$ are twice the sides of $Δ A B C$

DE = 6 cm, EF = 4 cm, DF = 5cm.

$∴$ Perimeter of $△$ DEF
= (DE + EF + DF) = 15 cm.

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