The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.

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Solution

It is given that $△ A B C ~ △ P Q R$ .
Therefore, the ratio of the areas of these triangles will be equal to the ratio of squares of their corresponding sides.
$\frac{ar (△ A B C)}{ar (△ P Q R)} = \frac{B C^{2}}{Q R^{2}} \Rightarrow \frac{9}{16} = \frac{4 . 5^{2}}{Q R^{2}} \Rightarrow Q R^{2} = \frac{4.5 \times 4.5 \times 16}{9} \Rightarrow Q R = \sqrt{\frac{4.5 \times 4.5 \times 16}{9}} = \frac{4.5 \times 4}{3} = 6 cm$

Hence, QR = 6 cm

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The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.

It is given that △ABC~△PQR. Therefore, the ratio of the areas of these triangles will be equal to the ratio of squares of their corresponding sides. ar(△ABC)ar(△PQR) = BC2QR2⇒ 916 = 4.52QR2⇒ QR2 = 4.5 × 4.5 × 169⇒ QR = 4.5 × 4.5 × 169 = 4.5 × 43= 6 cm Hence, QR = 6 cm