Longest Rod Across a Rectangular Park — Diagonal Length: A park measures 10 m by 8 m. What is the length of the longest pole (rod) that can be placed flat inside the park?
Aptitude
Area
Difficulty: Easy
Choose an option
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A10 metres
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B12.8 metres
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C13.4 metres
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D18 metres
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E12 metres
Answer
Correct Answer: 12.8 metres
Explanation
Introduction / Context:The longest straight object that can fit inside a rectangle lies along its diagonal. Therefore, the maximum pole length equals the rectangle's diagonal obtained by the Pythagorean theorem using the side lengths as perpendicular legs.
Given Data / Assumptions:
- Length = 10 m
- Breadth = 8 m
- Right-angle corner implies Pythagoras applies
Concept / Approach:For a rectangle with sides a and b, the diagonal d satisfies d^2 = a^2 + b^2. Compute the square root of the sum of squares to find d. This geometric maximum is independent of object orientation as any longer orientation would exceed the rectangle's bounds.
Step-by-Step Solution:
Compute squares: 10^2 = 100; 8^2 = 64.Sum: 100 + 64 = 164.Diagonal: d = √164 ≈ 12.806… m ≈ 12.8 m to one decimal place.Verification / Alternative check:
Compare alternatives: 12 m is too short (12^2 = 144 < 164); 13.4 m is too long (13.4^2 = 179.56 > 164).Why Other Options Are Wrong:
- 10 m equals one side, not the diagonal.
- 18 m far exceeds the rectangular dimension constraints.
- 12 m underestimates the true diagonal length.
Common Pitfalls:
- Forgetting that the diagonal is longer than either side but not longer than the hypotenuse computed via Pythagoras.
- Rounding early; carry enough precision before final rounding.
Final Answer:12.8 metres.