Three-side fencing of a rectangular field (one side open 20 ft): A rectangular field is fenced on three sides, leaving one 20-foot side uncovered. If the area is 680 sq ft, how many feet of fencing are required?

Introduction / Context:We have a rectangle with one known side (20 ft) left unfenced. Using the area, deduce the other side, then total the lengths to be fenced on the remaining three sides.

Given Data / Assumptions:

• One side (width) = 20 ft is open (unfenced).
• Area = 680 sq ft.
• Rectangle sides: let length = L, breadth = 20 ft.

Concept / Approach:From area, L = Area / breadth. Fenced sides are the two breadths plus the other length: total = 2L + 20.

Step-by-Step Solution:

Verification / Alternative check:Full perimeter would be 2(L + 20) = 2(34 + 20) = 108 ft; removing the open side (20 ft) yields 108 − 20 = 88 ft, same result.

Why Other Options Are Wrong:22, 44, 66 are too small; 108 corresponds to full perimeter, not three sides only.

Common Pitfalls:Accidentally fencing all four sides or subtracting the wrong side length from the perimeter.

Final Answer:88