Delta ABC sim Delta PQR for the correspondenc | vedclass

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Question

(A) Given that $\Delta ABC \sim \Delta PQR$. Since the triangles are similar,the ratios of their corresponding sides are equal: $\frac{AB}{PQ} = \frac

Vedclass · Accepted Answer

$PQ = 4.5, PR = 7.5$

Vedclass · Answer

(A) Given that $\Delta ABC \sim \Delta PQR$. Since the triangles are similar,the ratios of their corresponding sides are equal: $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$. Substituting the given values: $\frac{3}{PQ} = \frac{4}{6} = \frac{5}{PR}$. First,solve for $PQ$: $\frac{3}{PQ} = \frac{4}{6} \implies \frac{3}{PQ} = \frac{2}{3} \implies 2 \cdot PQ = 9 \implies PQ = 4.5$. Next,solve for $PR$: $\frac{4}{6} = \frac{5}{PR} \implies \frac{2}{3} = \frac{5}{PR} \implies 2 \cdot PR = 15 \implies PR = 7.5$. Thus,$PQ = 4.5$ and $PR = 7.5$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB = 3, BC = 4, AC = 5$ and $QR = 6$,find $PQ$ and $PR$.

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