If $△$ DEF $\sim$ $△$ ABC, AB = 4 cm, BC = 4 cm, CA = 3 cm and EF = 2 cm, then the perimeter of $△$ DEF is ____ cm.

5.5 cm

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7 cm

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6 cm

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2 cm

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Solution

The correct option is A 5.5 cm
Given $△$ DEF $\sim$ $△$ ABC.

$\Rightarrow \frac{A B}{D E} = \frac{A C}{D F} = \frac{B C}{E F}$

$\frac{4}{D E} = \frac{3}{D F} = \frac{4}{2} \Rightarrow \frac{4}{D E} = 2 and \frac{3}{D F} = 2$

$\Rightarrow D E = 2 cm and D F = 1.5 cm$

Perimeter of $△$ DEF = DE + EF+ FD
= 2 cm + 2 cm + 1.5 cm
= 5.5 cm

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If △ DEF ∼ △ABC, AB = 4 cm, BC = 4 cm, CA = 3 cm and EF = 2 cm, then the perimeter of △DEF is ____ cm.

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