Rectangle from diagonal and breadth: The diagonal of a rectangle is 17 cm and its breadth is 8 cm. Find its perimeter (in cm).
Aptitude
Area
Difficulty: Easy
Choose an option
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A92
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B46
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C42
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D84
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ENone of these
Answer
Correct Answer: 46
Explanation
Introduction / Context:Given a rectangle’s diagonal and one side, the other side follows from Pythagoras. The perimeter is then twice the sum of the two sides.
Given Data / Assumptions:
- Diagonal d = 17 cm.
- Breadth b = 8 cm.
Concept / Approach:Length l satisfies l^2 + b^2 = d^2. Solve for l, then compute perimeter P = 2(l + b).
Step-by-Step Solution:
l^2 = d^2 − b^2 = 17^2 − 8^2 = 289 − 64 = 225.l = 15 cm.Perimeter P = 2(l + b) = 2*(15 + 8) = 46 cm.Verification / Alternative check:Check back: 15^2 + 8^2 = 225 + 64 = 289 = 17^2 (consistent).
Why Other Options Are Wrong:92 and 84 double something else incorrectly; 42 undercounts.
Common Pitfalls:Using 2√(l^2 + b^2) as perimeter; that is incorrect—the perimeter is 2(l + b).
Final Answer:46