A rectangular field is to be fenced on three sides only, leaving one side of 20 ft completely uncovered.\nIf the area of the field is 680 sq ft, how many feet of fencing will be required?

Introduction:
This question tests combining rectangle area with partial perimeter (fencing on only three sides). The field has one side left uncovered, and that uncovered side is given as 20 ft. Using area = length * breadth, we can find the other dimension. Then, because only three sides are fenced, we do not take the full perimeter. Instead, we add the uncovered side’s opposite side (which is equal in length) and the two adjacent sides. This type of question checks whether you correctly interpret “three sides fenced” and do not accidentally compute full perimeter.

Given Data / Assumptions:

• Area of rectangle = 680 sq ft
• One side uncovered = 20 ft
• Let the uncovered side be the length L = 20 ft
• Breadth B = area / L
• Fencing required on three sides = L + 2B (since the opposite length side is fenced, and both breadth sides are fenced)

Concept / Approach:
Use area to find the missing dimension: B = 680/20. Then compute fencing as three sides. If the uncovered side is 20, the fenced sides are: the other 20 plus both breadths. Total fencing = 20 + B + B = 20 + 2B.

Step-by-Step Solution:
Given L (uncovered side) = 20 ftArea = L * B => 680 = 20 * BB = 680 / 20 = 34 ftFencing on three sides = 20 + 34 + 34Total fencing = 20 + 68 = 88 ft

Verification / Alternative Check:
Check area: 20*34 = 680 sq ft, correct. If we fenced all four sides, perimeter would be 2(20 + 34) = 108 ft. Since one 20 ft side is left open, fencing should be 108 - 20 = 88 ft, matching our direct three-side sum. This alternate method confirms the answer cleanly.

Why Other Options Are Wrong:
108 ft: is the full perimeter (fencing on all sides), not three sides.44 ft or 22 ft: ignores one or both breadth sides.11 ft: not consistent with the given area and side length.

Common Pitfalls:
Computing full perimeter even though only three sides are fenced.Using 20 as breadth instead of the uncovered side length.Forgetting opposite sides of a rectangle are equal.Arithmetic mistake in 680/20.

Final Answer:
88 ft