Rectangle with sides in the ratio 3:1 and perimeter 96 m: The length and breadth of a rectangle are in the ratio 3 : 1. If its total perimeter is 96 m, compute the exact length (in metres) of the rectangle.
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A36m
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B24m
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C12m
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D48m
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E40m
Answer
Correct Answer: 36m
Explanation
Introduction / Context:This is a standard perimeter-to-dimensions problem for rectangles using a given side ratio. We translate perimeter information into algebraic equations and then identify the rectangle’s length.
Given Data / Assumptions:
- Length : Breadth = 3 : 1 → Let length = 3k and breadth = 1k.
- Perimeter P = 96 m.
- Perimeter formula: P = 2 * (L + B).
Concept / Approach:Substitute the ratio-based expressions into the perimeter formula to solve for k, then compute the length 3k.
Step-by-Step Solution:
Let L = 3k and B = k.P = 2(L + B) = 2(3k + k) = 2(4k) = 8k.8k = 96 → k = 12.Therefore, length L = 3k = 3 * 12 = 36 m.Verification / Alternative check:With L = 36 m and B = 12 m, P = 2(36 + 12) = 2 * 48 = 96 m, which matches the given perimeter.
Why Other Options Are Wrong:24m and 12m are the breadth or its multiples; 48m and 40m do not satisfy the ratio and perimeter simultaneously.
Common Pitfalls:Forgetting to double the sum in the perimeter formula or mixing up length and breadth magnitudes (3k vs k).
Final Answer:36m