\(\Delta ABC \sim \Delta PQR\), \(A(\Delta ABC) = 80\) cm\(^2\), \(A(\Delta PQR) = 125\) cm\(^2\) and AB = 8 cm. Find PQ.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: PQ = 10 cm

By the theorem of areas of similar triangles, \(\dfrac{A(\Delta ABC)}{A(\Delta PQR)} = \dfrac{AB^2}{PQ^2}\).

\(\dfrac{80}{125} = \dfrac{16}{25} = \dfrac{8^2}{PQ^2}\) \(\therefore \dfrac{8}{PQ} = \dfrac{4}{5}\) \(\therefore PQ = 10\) cm.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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