Equal areas – Square vs rectangle with offset sides: A square and a rectangle have equal area. The rectangle’s length is 5 cm more than the square’s side; its breadth is 3 cm less than the square’s side. Find the rectangle’s perimeter.
Aptitude
Area
Difficulty: Medium
Choose an option
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A15 cm
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B18 cm
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C34 cm
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D26 cm
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ENone of these
Answer
Correct Answer: 34 cm
Explanation
Introduction / Context:Let the square side be x. The rectangle’s dimensions become (x + 5) and (x − 3). Equal areas give an equation to solve for x, and hence perimeter.
Given Data / Assumptions:
- Square side = x cm.
- Rectangle: length = x + 5; breadth = x − 3.
Concept / Approach:Set x^2 = (x + 5)(x − 3) and solve for x; compute perimeter P = 2[(x + 5) + (x − 3)].
Step-by-Step Solution:
x^2 = x^2 + 2x − 15 ⇒ 2x − 15 = 0 ⇒ x = 7.5 cm.Rectangle L = 12.5 cm, B = 4.5 cm.Perimeter = 2(12.5 + 4.5) = 2 * 17 = 34 cm.Verification / Alternative check:Area check: square 7.5^2 = 56.25; rectangle 12.5 * 4.5 = 56.25 ✔️
Why Other Options Are Wrong:15, 18, 26 come from miscomputing x or forgetting to double for perimeter.
Common Pitfalls:Sign errors when expanding (x + 5)(x − 3); arithmetic errors with decimals.
Final Answer:34 cm