ΔABC ~ ΔPQR, if AB = 6, BC = 4, AC = 8 and PR = 6, then PQ + QR = �

1.	ΔABC ~ ΔPQR, if AB = 6, BC = 4, AC = 8 and PR = 6, then PQ + QR = …………(A) 8(B) 10 (C) 7.5 (D) 9
Answer» Correct option is (C) 7.5 Given that \(\triangle ABC \sim \triangle PQR \) Then their corresponding sides are in the same ratio. \(\therefore\) \(\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}\) \(\because\) \(\frac{AB}{PQ}=\frac{AC}{PR}\) \(\Rightarrow\) \(PQ=AB\times\frac{PR}{AC}\) \(=6\times\frac68\) \((\because AB=6,PR=6\;\&\;AC=8)\) \(=\frac92=4.5\) & \(\frac{BC}{QR}=\frac{AC}{PR}\) \(\Rightarrow\) \(QR=BC\times\frac{PR}{AC}\) \(=4\times\frac68\) \((\because BC=4,PR=6\;\&\;AC=8)\) \(=\frac62=3\) \(\therefore PQ+QR=4.5+3=7.5\) Correct option is: (C) 7.5

ΔABC ~ ΔPQR, if AB = 6, BC = 4, AC = 8 and PR = 6, then PQ + QR = …………(A) 8(B) 10 (C) 7.5 (D) 9

Answer»

Correct option is (C) 7.5

Given that \(\triangle ABC \sim \triangle PQR \)

Then their corresponding sides are in the same ratio.

\(\therefore\) \(\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}\)

\(\because\) \(\frac{AB}{PQ}=\frac{AC}{PR}\)

\(\Rightarrow\) \(PQ=AB\times\frac{PR}{AC}\)

\(=6\times\frac68\) \((\because AB=6,PR=6\;\&\;AC=8)\)

\(=\frac92=4.5\)

& \(\frac{BC}{QR}=\frac{AC}{PR}\)

\(\Rightarrow\) \(QR=BC\times\frac{PR}{AC}\)

\(=4\times\frac68\) \((\because BC=4,PR=6\;\&\;AC=8)\)

\(=\frac62=3\)

\(\therefore PQ+QR=4.5+3=7.5\)

Correct option is: (C) 7.5