Fencing a rectangle: The length of a rectangular plot is 20 m more than its breadth. If total fencing cost at Rs 26.50 per metre is Rs 5300, find the length of the plot (in metres).
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A40
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B20
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C30
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Dnone of these
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E50
Answer
Correct Answer: none of these
Explanation
Introduction / Context:This is perimeter-from-cost, then dimensions-from-perimeter algebra, concluding with identification of the correct length among options.
Given Data / Assumptions:
- Cost = Rs 5300
- Rate = Rs 26.50 per m
- L = B + 20
Concept / Approach:Perimeter P = Cost / Rate. For a rectangle, P = 2(L + B). With L = B + 20, solve for B and then L.
Step-by-Step Solution:
P = 5300 / 26.5 = 200 mL + B = P/2 = 100(B + 20) + B = 100 → 2B = 80 → B = 40 → L = 60Verification / Alternative check:Perimeter check: 2*(60+40) = 2*100 = 200; Cost check: 200*26.5 = 5300. All consistent.
Why Other Options Are Wrong:40, 20, 30, 50 are not the computed length; correct length is 60, which is not listed; therefore “none of these”.
Common Pitfalls:Forgetting to divide perimeter by 2 or misdividing 5300 by 26.5 (it equals 200 exactly).
Final Answer:none of these