Fencing three sides of a rectangle: A rectangular field has one 20 ft side left unfenced. If the area is 680 sq. ft, how many feet of fencing are required for the other three sides?
Aptitude
Area
Difficulty: Medium
Choose an option
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A22
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B44
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C66
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D88
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ENone of these
Answer
Correct Answer: 88
Explanation
Introduction / Context:We know the area and that one side of 20 ft is open (no fence). Using area, we can find the other dimension; then the fencing equals the sum of the remaining three sides.
Given Data / Assumptions:
- One side (length) = 20 ft (unfenced).
- Area = 680 sq. ft ⇒ 20 × width = 680.
- Fencing needed = the other 20 ft side + both widths.
Concept / Approach:Compute width from area, then sum three sides (20 + width + width). Avoid mixing up which side is open; the open side is specifically the 20 ft side.
Step-by-Step Solution:
width w = 680 / 20 = 34 ft.Fencing required = 20 + 34 + 34 = 88 ft.Verification / Alternative check:
Full perimeter would be 2(20 + 34) = 108, minus the open 20 gives 88; matches.Why Other Options Are Wrong:
22, 44, 66 are partial sums; they do not account for all three fenced sides.Common Pitfalls:
Subtracting the wrong side from the full perimeter or miscalculating width from area.Final Answer:
88