Rectangle with breadth 75% of length: The breadth is 75% of the length. If the rectangle’s perimeter is 1050 m, find its area (in sq. m).
Aptitude
Area
Difficulty: Easy
Choose an option
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A65700 sq.m
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B54500 sq.m
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C78700 sq.m
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D67500 sq.m
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ENone of these
Answer
Correct Answer: 67500 sq.m
Explanation
Introduction / Context:Similar to related problems, a perimeter and a fixed proportional relation between sides allow us to solve for each dimension and then compute area.
Given Data / Assumptions:
- B = 0.75L.
- Perimeter P = 1050 ⇒ 2(L + B) = 1050 ⇒ L + B = 525.
Concept / Approach:Substitute B = 0.75L into L + B = 525 to solve for L, then compute B and multiply to get the area.
Step-by-Step Solution:
L + 0.75L = 525 ⇒ 1.75L = 525 ⇒ L = 300 m.B = 0.75 × 300 = 225 m.Area = L * B = 300 * 225 = 67,500 sq. m.Verification / Alternative check:
Perimeter check: 2(300 + 225) = 2(525) = 1050 ✔Why Other Options Are Wrong:
65700, 54500, 78700 are not the product of 300 and 225 and typically stem from arithmetic mistakes.Common Pitfalls:
Treating 75% as 0.75 is essential; mixing percentage handling often causes errors.Final Answer:
67500 sq.m