Complete the following activities and rewrite it:
(i) If $△ A B C \sim △ P Q R, A (△$
$A B C) = 81 {c m}^{2}, A (△ P Q R) =$ $121 {c m}^{2}, B C = 6.3 c m$ , then complete the following activity to find QR.
Activity :
$△ A B C \sim △ P Q R \dots \dots$ (given)
$\begin{matrix} ∴ \frac{A (△ A B C)}{A (△ P Q R)} = \frac{□}{{Q R}^{2}} \dots \dots \dots \dots ∴ \frac{□}{121} = \frac{(6.3)^{2}}{{Q R}^{2}} ∴ \frac{□}{11} = \frac{6.3}{Q R} \dots \dots . (Taking square root of both sides) Q R = \frac{6.3 \times 11}{□} Q R = □ c m \end{matrix}$

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Solution

$△ A B C = △ P Q R$
If two $Δ$ are similar ratio of area of two $Δ$ is equal to ratio of squares of corresponding sides.
ar $\frac{A B C}{P Q R} = \frac{81}{121}$
$\begin{matrix} \frac{81}{121} = \frac{B C^{2}}{Q R^{2}} \frac{9}{11} = \frac{6.3}{Q R} Q R = \frac{6.3 \times 11}{9} Q R = 7.7 c m \end{matrix}$

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