In $△ P Q R,$ $P Q = 4$ cm, $Q R = 3$ cm, and $R P = 3.5$ cm. $△ D E F$ is similar to $△ P Q R .$ If $E F = 9$ cm, then what is the perimeter of $△ D E F ?$

10.5

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21

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31.5

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Solution

The correct option is C $31.5$ cm
$P Q = 4, Q R = 3$ and $R P = 3.5$
Also, $E F = 9$
Now, perimeter of $△ P Q R = P Q + Q R + R P = 4 + 3 + 3.5 = 10.5$
Given, $△ D E F \sim △ P Q R$
$\frac{E F}{Q R} = \frac{P e r i m e t e r (△ D E F)}{P e r i m e t e r (△ P Q R)}$
$\frac{9}{3} = \frac{P e r i m e t e r (△ D E F)}{10.5}$
Perimeter $(△ D E F) = 31.5$ cm

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In △PQR, PQ=4 cm, QR=3 cm, and RP=3.5 cm. △DEF is similar to △PQR. If EF=9 cm, then what is the perimeter of △DEF?

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