A rectangular field is to be fenced on three sides leaving a side of 20 feet…

Concept: For a rectangle, Area = Length × Width. When only three sides are fenced and one side of known length is left open, the fencing needed equals the open side's length plus twice the other (perpendicular) dimension — Fencing = L_open + 2 × (Area ÷ L_open).

Application:

1. The uncovered side is 20 feet, so take this as one dimension of the field: L = 20 ft.

2. Since Area = L × W = 680 sq ft, the other dimension is W = 680 ÷ 20 = 34 ft.

3. Fencing covers the side opposite the uncovered one (also 20 ft) plus the two perpendicular sides (34 ft each): Fencing = 20 + 34 + 34 = 88 ft.

Cross-check: 20 × 34 = 680 sq ft, matching the given area, so the dimensions are consistent. Assigning the uncovered side to the other dimension instead (making it about 34 ft) would need the remaining side to be roughly 20 ft, giving fencing of 34 + 2×20 = 74 ft — not among the offered values — confirming the 20 ft side is the one left uncovered, exactly as stated.

Result: 88 feet of fencing is required.