Fencing three sides of a rectangle:\nA 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?

Difficulty: Medium

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

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