A rectangular field is to be fenced on three sides, leaving one side of length 20 feet uncovered. If the area of the field is 680 square feet, how many feet of fencing are required?

Introduction / Context:
This question is a mix of area and perimeter concepts for rectangles. It is common in aptitude tests where candidates must relate the area of a field to its sides and then determine the length of fencing required for part of its boundary. Here, only three sides of the rectangular field are fenced, and one side is left open, which adds a small twist to the usual perimeter calculation.

Given Data / Assumptions:
• The field is rectangular.• One side of the rectangle, left unfenced, has length 20 ft.• Area of the field = 680 square feet.• We need to find the total length of fencing for the remaining three sides.

Concept / Approach:
Let the length of the field be L and the breadth be B. The area is L * B. One side of 20 ft is given as the side left uncovered. We assume that this side corresponds to length L = 20 ft. Then the breadth B can be found from the area relation. The total fencing required is the sum of the other three sides: one more length and two breadths, so fencing = L + 2B. We simply compute B using the area and then compute this expression.

Step-by-Step Solution:
Step 1: Assign the known side.Let L = 20 ft be the side left unfenced.Step 2: Use the area formula.Area = L * B = 680 sq. ft.20 * B = 680.Step 3: Solve for B.B = 680 / 20 = 34 ft.Step 4: Compute the length of fencing required.Fencing length = L + 2B = 20 + 2 * 34.2 * 34 = 68.Fencing length = 20 + 68 = 88 ft.

Verification / Alternative check:
We can verify the area using the calculated breadth. With L = 20 ft and B = 34 ft, the area is 20 * 34 = 680 square feet, which matches the given data. The three fenced sides are 34 ft, 34 ft, and 20 ft, whose sum is 88 ft. This confirms that the fencing length is computed correctly and is internally consistent with the problem statement.

Why Other Options Are Wrong:
Option A: 34 ft corresponds only to one breadth and ignores the other sides.Option B: 40 ft does not match any reasonable combination of sides for a field of area 680 sq. ft.Option C: 68 ft accounts only for the two breadths and neglects the remaining length that must be fenced.

Common Pitfalls:
Some learners mistakenly compute the full perimeter 2(L + B) instead of just three sides, which would give 2(20 + 34) = 108 ft and does not match any option. Others may mix up which side is left unfenced. Carefully interpreting the phrase "fenced on three sides" and explicitly writing the expression L + 2B avoids these misunderstandings.

Final Answer:
The total length of fencing required is 88 feet.