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

Problem restatementOne side of the rectangle (length 20 ft) is left unfenced; the other three sides are fenced. Given the area, find the fenced length.

Given data

• Uncovered side (take as length) = 20 ft.
• Area = 680 sq ft.

Concept/ApproachLet breadth be b. Then area = length × breadth = 20 × b.

Step-by-Step calculation 20 × b = 680 ⇒ b = 680 / 20 = 34 ft Fenced sides = other length (20 ft) + two breadths (2 × 34 ft) Total fencing = 20 + 68 = 88 ft

Verification/AlternativeIf instead the uncovered side were a breadth, you would first compute the corresponding length, but the statement specifies the uncovered side is 20 ft, matching the calculation above.

Common pitfalls

• Using the full perimeter 2(L + B); remember only three sides are fenced.

Final Answer88 ft