Rectangle with breadth as a percent of length: The breadth of a rectangle equals 60% of its length. If the perimeter is 800 m, find the area (in sq. m) of the field.

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

Accepted Answer

Introduction / Context:Linking perimeter to dimensions is standard: perimeter fixes the sum of length and breadth. Given a percentage relation between breadth and length, we can solve for both and compute area. Given Data / Assumptions: B = 0.60L. Perimeter P = 800 m ⇒ 2(L + B) = 800. Area A = L * B. Concept / Approach:Use the perimeter equation to find L + B, substitute B = 0.60L, solve for L, then compute B and multiply to obtain area. Step-by-Step Solution: 2(L + B) = 800 ⇒ L + B = 400.With B = 0.60L: L + 0.60L = 400 ⇒ 1.60L = 400 ⇒ L = 250 m.Then B = 0.60 * 250 = 150 m.Area A = L * B = 250 * 150 = 37500 sq. m. Verification / Alternative check: Perimeter check: 2(250 + 150) = 2 * 400 = 800 ✔ Why Other Options Are Wrong: 47500, 57500, 77500 come from incorrect algebra or misusing percentages. Common Pitfalls: Using 60 as a fraction instead of 0.60.Forgetting to halve the perimeter to get L + B. Final Answer: 37500

Rectangle with breadth as a percent of length: The breadth of a rectangle equals 60% of its length. If the perimeter is 800 m, find the area (in sq. m) of the field.

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