Difficulty: Easy
Correct Answer: 36 m
Explanation:
Introduction / Context:
This is a straightforward ratio and perimeter question about a rectangle. Knowing the ratio of length to breadth allows us to express both dimensions in terms of a single variable. The perimeter formula then gives an equation in that variable. Solving it provides the actual dimensions, and we are asked specifically for the length in metres.
Given Data / Assumptions:
Concept / Approach:
Let length L = 3x and breadth B = x. Substitute these into the perimeter formula. By equating 2(L + B) to 96, we can solve for x and then compute L. The method is a direct application of ratios and a single linear equation, suitable for rapid mental or written calculation.
Step-by-Step Solution:
Let L = 3x and B = x.Perimeter P = 2(L + B) = 2(3x + x) = 2(4x) = 8x.Given P = 96, so 8x = 96.x = 96 / 8 = 12.Length L = 3x = 3 * 12 = 36 m.Breadth B = x = 12 m (for completeness).
Verification / Alternative check:
Check the perimeter: 2(L + B) = 2(36 + 12) = 2 * 48 = 96 m, which matches the given value. The ratio L : B = 36 : 12 simplifies to 3 : 1, which also matches the question. Both checks show that the value 36 m is consistent and correct.
Why Other Options Are Wrong:
24 m and 12 m are actually values associated with breadth, not length, and do not satisfy the 3:1 ratio if taken as length. 48 m would make the breadth 16 m, giving a perimeter 2(48 + 16) = 128 m, which is too large. 30 m does not fit the ratio 3:1 with any integer breadth that yields perimeter 96 m.
Common Pitfalls:
Some learners mistakenly assume the ratio directly gives the values, for example taking length as 3 m and breadth as 1 m and then scaling incorrectly. Others mix up which side corresponds to 3 parts and which to 1 part. Also, forgetting that perimeter is 2(L + B) can lead to errors like using L + B = 96 instead of 2(L + B) = 96.
Final Answer:
36 m
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