If the ratio of the corresponding sides of two similar triangles is $3 : 4$ , then the ratio of their perimeters is:

3 : 4

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4 : 3

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9 : 16

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16 : 9

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Solution

The correct option is A $3 : 4$
Ratio corresponding to similar triangle $= \frac{3}{4}$
$i . e . \frac{A B}{P Q} = \frac{3}{4} \frac{B C}{Q R} = \frac{3}{4} \frac{A C}{P R} = \frac{3}{4} A B = \frac{3 P Q}{4} B C = \frac{3 Q R}{4} A C = \frac{3 P R}{4} \frac{P e r i m e t e r o f A B C}{P e r i m e t e r o f P Q R} = \frac{A B + B C + C A}{P Q + Q R + R P} = \frac{\frac{3}{4} (P Q + Q R + P R)}{P Q + Q R + P R} = \frac{3}{4}$

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If the ratio of the corresponding sides of two similar triangles is 3:4, then the ratio of their perimeters is:

The correct option is A 3:4Ratio corresponding to similar triangle =34 i.e.ABPQ=34BCQR=34ACPR=34AB=3PQ4BC=3QR4AC=3PR4PerimeterofABCPerimeterofPQR=AB+BC+CAPQ+QR+RP=34(PQ+QR+PR)PQ+QR+PR=34

If the ratio of the corresponding sides of two similar triangles is $3 : 4$ , then the ratio of their perimeters is: