Difficulty: Hard
Correct Answer: 2520 sq m
Explanation:
Introduction / Context:This problem tests solving rectangle dimensions using a system of two linear equations derived from perimeter and difference. Once length and breadth are obtained, area is computed using length * breadth. The core skill is translating words into equations correctly: perimeter gives l + b, and difference gives l - b.
Given Data / Assumptions:
Concept / Approach:From perimeter, compute l + b. Combine with l - b to solve for l and b. Then multiply to get area.
Step-by-Step Solution:
Step 1: From perimeter: 2 * (l + b) = 206 => l + b = 103 Step 2: Also given: l - b = 23 Step 3: Add equations: (l + b) + (l - b) = 103 + 23 => 2l = 126 Step 4: l = 63 m Step 5: Substitute into l + b = 103 => 63 + b = 103 => b = 40 m Step 6: Area = l * b = 63 * 40 = 2520 sq mVerification / Alternative check:Check difference: 63 - 40 = 23 m, correct. Check perimeter: 2*(63+40) = 2*103 = 206 m, correct. Therefore the derived area 63*40 is reliable and must be correct.
Why Other Options Are Wrong:
2420, 2320: too low and would require smaller dimension products than 63*40. 2620, 2720: too high and would require larger products while still matching the fixed perimeter and difference, which is not possible. Only one unique rectangle matches both l+b and l-b, so only one area is possible.Common Pitfalls:Common mistakes include forgetting to divide by 2 when converting perimeter to l + b, reversing length and breadth in the difference, or subtracting equations incorrectly. Another error is using area = 2(l+b) which is actually perimeter, not area.
Final Answer:2520 sq m
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