Rectangle transformation: The length of a rectangle is twice its breadth. If length is decreased by 5 cm and breadth is increased by 5 cm, the area increases by 75 sq cm. Find the original length of the rectangle.
Aptitude
Area
Difficulty: Medium
Choose an option
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A10cm
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B20cm
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C30cm
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D40cm
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E35cm
Answer
Correct Answer: 40cm
Explanation
Introduction / Context:This algebra problem involves relating original dimensions to changed dimensions and comparing areas to find unknowns.
Given Data / Assumptions:
- L = 2B (original)
- (L - 5) * (B + 5) = L * B + 75
- All lengths in cm; rectangle properties standard.
Concept / Approach:Expand the changed-area expression, simplify, and use L = 2B to solve a linear system for B and L.
Step-by-Step Solution:
(L - 5)(B + 5) = LB + 75LB + 5L - 5B - 25 = LB + 755L - 5B - 25 = 75 → 5(L - B) = 100 → L - B = 20Given L = 2B → 2B - B = 20 → B = 20L = 2B = 40Verification / Alternative check:Original area LB = 40*20 = 800. New area (35*25) = 875. Increase = 75 sq cm, matches the condition.
Why Other Options Are Wrong:10cm, 20cm, 30cm, 35cm do not satisfy both L = 2B and L - B = 20 simultaneously.
Common Pitfalls:Dropping terms during expansion or mixing the sign in L - B; also, assuming both changes are equal but forgetting L = 2B.
Final Answer:40cm