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Question: 7. $\triangle PQR \sim \triangle XYZ$ and the perimeters of $\triangle PQR$ and $\triangle XYZ$ are ...

  1. △PQR∼△XYZ\triangle PQR \sim \triangle XYZ and the perimeters of △PQR\triangle PQR and △XYZ\triangle XYZ are 30 cm and 18 cm respectively. If QR = 9 cm, then, YZ is equal to
A

4.5 cm.

B

5.4 cm.

C

12.5 cm.

D

9.5 cm.

Answer

5.4 cm.

Explanation

Solution

Since the triangles are similar, the ratio of any two corresponding sides is constant and equal to the ratio of their perimeters.

Scale Factor=Perimeter of △XYZPerimeter of △PQR=1830=35\text{Scale Factor} = \frac{\text{Perimeter of } \triangle XYZ}{\text{Perimeter of } \triangle PQR} = \frac{18}{30} = \frac{3}{5}

Given QR=9QR = 9 cm corresponds to YZYZ. So,

YZ=35×9=275=5.4 cmYZ = \frac{3}{5} \times 9 = \frac{27}{5} = 5.4 \text{ cm}