Question 60

Let $$\triangle ABC \sim \triangle QPR and \frac{ar(\triangle ABC)}{ar(\triangle PQR)} = \frac{9}{16}$$. If AB = 12 cm, BC = 6 cm and AC = 9 cm,then QR is equal to:

Solution

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides

$$\frac{ar(\triangle ABC)}{ar(\triangle PQR)}=\frac{BC^2}{QR^2}$$

$$\frac{9}{16}=\frac{36}{QR^2}$$

$$QR^2=64$$

QR = 8 cm.

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