Q.3 (B)(4) If Δ PQR sim Δ LMN , 9 × A(Δ PQR) = 16 × A(Δ LMN) and QR = 20, then find MN.

If \(\Delta PQR \sim \Delta LMN\), \(9 \times A(\Delta PQR) = 16 \times A(\Delta LMN)\) and QR = 20, then find MN.

Q.3 (B)(4) If \(\Delta PQR \sim \Delta LMN\), \(9 \times A(\Delta PQR) = 16 \times A(\Delta LMN)\) and QR = 20, then find MN.

Doubtly Asked 25 Oct 2026 ssc 10th Save WhatsApp Report

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Answer: MN = 15

\(9 \times A(\Delta PQR) = 16 \times A(\Delta LMN)\), so \(\dfrac{A(\Delta PQR)}{A(\Delta LMN)} = \dfrac{16}{9}\).

For similar triangles the ratio of areas equals the ratio of the squares of corresponding sides: \(\dfrac{QR^2}{MN^2} = \dfrac{16}{9}\), so \(\dfrac{QR}{MN} = \dfrac{4}{3}\).

\(\therefore MN = \dfrac{3}{4}\times 20 = 15\).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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If \(\Delta PQR \sim \Delta LMN\), \(9 \times A(\Delta PQR) = 16 \times A(\Delta LMN)\) and QR = 20, then find MN.

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