Rectangular field – Ratio 5:4 and breadth is 20 m less than length: In a rectangle, length : breadth = 5 : 4, and the breadth is 20 m less than the length. Find the perimeter (in metres).

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Use ratio relations with a given difference to find actual dimensions, then compute perimeter P = 2(L + B). Given Data / Assumptions: L : B = 5 : 4 ⇒ L = 5k, B = 4k. B = L − 20 ⇒ 4k = 5k − 20. Concept / Approach:Solve for k, then compute L, B, and perimeter. Step-by-Step Solution: 4k = 5k − 20 ⇒ k = 20.L = 5k = 100 m; B = 4k = 80 m.Perimeter = 2(100 + 80) = 360 m (intermediate).But the statement says breadth is 20 m less than length; with L = 100, B = 80 (20 m less) is correct; perimeter becomes 360 m. Verification / Alternative check:Direct substitution confirms the condition; however, since the provided keyed answers commonly map to 260 m when the difference is 10k = 20 ⇒ k = 2, this mismatch indicates an option set discrepancy. For the current corrected arithmetic, the perimeter is 360 m. Why Other Options Are Wrong:260 m and 280 m correspond to different difference values; given data leads to 360 m. Common Pitfalls:Interpreting 'less than' inversely; mishandling the ratio. Final Answer:360m

Rectangular field – Ratio 5:4 and breadth is 20 m less than length: In a rectangle, length : breadth = 5 : 4, and the breadth is 20 m less than the length. Find the perimeter (in metres).

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