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Home » The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR.
The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR.
CBSE | Class 10 | Exercise 4C | Maths | RS Aggarwal | Triangles
The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR.

Answer:

Given,

∆ ABC ~ ∆ PQR

The ratio of the areas of triangles will be equal to the ratio of squares of their corresponding sides.

(1)   \begin{equation*} \frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\Delta P Q R)}=\frac{B C^{2}}{Q R^{2}} \end{equation*}

(2)   \begin{equation*} \begin{array}{l} \frac{9}{16}=\frac{4^{2}}{Q R^{2}} \\ Q R^{2}=\frac{4.5 \times 4.5 \times 16}{9} \\ Q R=\sqrt{\frac{(4.5 \times 4.5 \times 16)}{9}} \\ Q R=\frac{4.5 \times 4}{3} \\ \therefore Q R=6 \mathrm{~cm} \end{array} \end{equation*}

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