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  • The areas of two similar triangles ABC and PQR are 25 cm2 and 49 cm2 respectively. If QR = 8.4 cm, find BC in cm.Option

The areas of two similar triangles ABC and PQR are 25 cm2 and 49 cm2 respectively. If QR = 8.4 cm, find BC in cm.

Option: 1

5 cm


Option: 2

6 cm


Option: 3

7 cm


Option: 4

8 cm


Answers (1)

best_answer

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

\\\therefore \quad \frac{\operatorname{ar}(\Delta A B C)}{\operatorname{ar}(\Delta P Q R)}=\frac{B C^{2}}{Q R^{2}} \\ \\\Rightarrow \quad\left(\frac{B C}{Q R}\right)^{2}=\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\Delta P Q R)}=\frac{25}{49}=\left(\frac{5}{7}\right)^{2} \\ \\\Rightarrow \frac{B C}{Q R}=\frac{5}{7} \Rightarrow \frac{B C}{8.4}=\frac{5}{7}

\Rightarrow \quad B C=\frac{5 \times 8.4}{7} cm =5 \times 1.2 cm =6 cm

Posted by

Deependra Verma

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