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Question

$$\Delta ABC$$ is similar to $$\Delta PQR$$, ar($$\Delta ABC$$) = 36 sq. cm. and ar($$\Delta PQR$$) =49 sq.cm. If BC = 12 cm, find QR.


Solution

$$\because \Delta ABC \sim \Delta PQR$$
$$\displaystyle \therefore \dfrac{ar(\Delta ABC)}{ar(\Delta PQR)} = \dfrac{BC^2}{QR^2}$$
$$\displaystyle \Rightarrow \dfrac{36}{49} = \dfrac{12^2}{QR^2}$$
$$\displaystyle \Rightarrow (QR)^2 = \dfrac{12 \times 12 \times 49}{36} = 4 \times 49$$
$$\Rightarrow QR = + \sqrt{4 \times 49}$$
$$= 2 \times 7 = 14 cm$$


1154706_345944_ans_015c7fea23b14d5981a3bf04578ec4eb.jpg

Mathematics

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