Question 69

$$\triangle$$ABC $$\sim$$ $$\triangle$$QPR and AB = 8 cm, BC = 12 cm and AC = 6 cm. If ar($$\triangle$$ABC) : ar($$\triangle$$PQR) = 16 : 25, then RQ 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.

$$\frac{\left(area\ of\ \triangle\ ABC\right)}{area\ of\ \triangle\ PQR\ }=\left(\frac{BC}{QR}\right)^2$$

$$\frac{16}{25}=\left(\frac{AC}{QR}\right)^2$$

$$\frac{6}{QR}=\frac{4}{5}$$

$$QR=\frac{30}{4}$$

$$QR=7.5$$

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