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

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Solution

The correct option is A
18

Given $△$ DEF $\sim$ $△$ ABC.

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

$\frac{4}{D E} = \frac{3}{D F} = \frac{2}{4} = \frac{1}{2}$

$\frac{P e r i m e t e r (△ A B C)}{P e r i m e t e r (△ D E F)} = \frac{1}{2}$

$\frac{9}{P e r i m e t e r (△ D E F)} = \frac{1}{2}$ .......(ratio of perimeters of similar triangles)

$P e r i m e t e r (△ D E F)$ = 18 cm

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The correct option is A 18 Given △ DEF ∼ △ABC. ABDE=ACDF=BCEF 4DE=3DF=24 =12 Perimeter (△ABC)Perimeter (△DEF)=12 9Perimeter (△DEF)=12 .......(ratio of perimeters of similar triangles) Perimeter (△DEF) = 18 cm

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