Rectangle with given perimeter and difference: The difference between the length and breadth of a rectangle is 23 m, and its perimeter is 206 m. Find the area of the rectangle.
Aptitude
Area
Difficulty: Easy
Choose an option
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A2520
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B2420
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C2320
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D2620
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E2300
Answer
Correct Answer: 2520
Explanation
Introduction / Context:This question checks algebraic handling of perimeter and difference constraints for rectangles, followed by area calculation.
Given Data / Assumptions:
- L - B = 23 m
- Perimeter P = 206 m
- Rectangle perimeter formula: P = 2(L + B)
Concept / Approach:From P = 2(L + B) we get L + B. With a system L + B and L - B, solve for L and B, then compute area = L * B.
Step-by-Step Solution:
L + B = 206 / 2 = 103L - B = 23Add: 2L = 126 → L = 63Then B = 103 - 63 = 40Area = L * B = 63 * 40 = 2520 sq mVerification / Alternative check:Check difference: 63 - 40 = 23. Check perimeter: 2*(63+40) = 2*103 = 206. Consistent.
Why Other Options Are Wrong:2420, 2320, 2620, 2300 do not match L*B given the exact L and B derived from both equations.
Common Pitfalls:Using P instead of P/2 for L+B or mixing up which is larger (length vs breadth) leads to wrong numbers.
Final Answer:2520