If Delta ABC sim Delta PQR for the correspond | vedclass

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(C) Given that $\Delta ABC \sim \Delta PQR$,the ratio of their corresponding sides is equal to the ratio of their perimeters.Let the perimeter of $\De

Vedclass · Accepted Answer

$\frac{4}{5} ; \frac{4}{5}$

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(C) Given that $\Delta ABC \sim \Delta PQR$,the ratio of their corresponding sides is equal to the ratio of their perimeters.Let the perimeter of $\Delta ABC$ be $P_1 = 48$ and the perimeter of $\Delta PQR$ be $P_2 = 60$.The ratio of corresponding sides is $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} = \frac{P_1}{P_2} = \frac{48}{60} = \frac{4}{5}$.Thus,$\frac{AB}{PQ} = \frac{4}{5}$.For the second ratio,using the property of equal ratios: if $\frac{a}{b} = \frac{c}{d} = k$,then $\frac{a+c}{b+d} = k$.Therefore,$\frac{AB + BC}{PQ + QR} = \frac{AB}{PQ} = \frac{4}{5}$.Both ratios are equal to $\frac{4}{5}$.

If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$,and the perimeter of $\Delta ABC$ is $48$ while the perimeter of $\Delta PQR$ is $60$,find the ratios $\frac{AB}{PQ}$ and $\frac{AB + BC}{PQ + QR}$.

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