Given $△$ DEF $\sim$ $△$ ABC. If AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, then the perimeter of $△$ DEF is ____.

16 cm

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15 cm

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20 cm

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17 cm

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Solution

The correct option is B
15 cm

Given $△$ DEF $\sim$ $△$ ABC.

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

$\frac{3}{D E} = \frac{2.5}{D F} = \frac{2}{4} = \frac{1}{2}$

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

$\frac{7.5}{P e r i m e t e r (△ D E F)} = \frac{1}{2}$ .......(ratio of perimeters of similar triangles)

$P e r i m e t e r (△ D E F)$ = 15 cm

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Given △ DEF ∼ △ABC. If AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, then the perimeter of △DEF is ____.

The correct option is B 15 cm Given △ DEF ∼ △ABC. ABDE=ACDF=BCEF 3DE=2.5DF=24 =12 Perimeter (△ABC)Perimeter (△DEF)=12 7.5Perimeter (△DEF)=12 .......(ratio of perimeters of similar triangles) Perimeter (△DEF) = 15 cm

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