In $△$ ABC, 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

Since the two triangles are similar, ratios of the corresponding sides will be equal.
$\frac{A B}{D E}$ = $\frac{A C}{D F}$ = $\frac{B C}{E F}$ = $\frac{2}{4}$ = $\frac{1}{2}$

DE = 2AB,
DE = 6 cm,
DF = 2AC,
DF = 5 cm.

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

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