Question

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

• A. 68
• B. 88
• C. 108
• D. 58

Answer 1

Answer:

B. 88

Key Information Provided:

• The field is rectangular.

• One side, measuring 20 feet, is not to be fenced.

• The total area of the field is 680 square feet.

Mathematical Approach

1. Define Variables:

• Let the length of the rectangular field be l feet.

• Let the width of the rectangular field be w feet.

2. Formulate Equations based on given information:

• Area of a rectangle: Area = length × width. So, l × w = 680.

• Fencing requirement: The fencing is on three sides. Since one side of 20 feet is left uncovered, this implies that this 20 feet side is either the length or the width. Let's assume the uncovered side is one of the lengths (l). Therefore, the fencing will cover the other length (l) and both widths (w + w). The total fencing required would be l + 2w.

3. Determine the unfenced side:

• The problem states a side of 20 feet is left uncovered. This means either l = 20 or w = 20.

• Case 1: If the length (l) is 20 feet.

  • Using the area formula: 20 × w = 680.

  • Solving for w: w = 680 / 20 = 34 feet.

  • Fencing required = l + 2w = 20 + 2(34) = 20 + 68 = 88 feet.

• Case 2: If the width (w) is 20 feet.

  • Using the area formula: l × 20 = 680.

  • Solving for l: l = 680 / 20 = 34 feet.

  • In this case, the uncovered side is 20 feet (width). The fencing would cover the other width (w) and both lengths (l + l). The total fencing required would be w + 2l.

  • Fencing required = 20 + 2(34) = 20 + 68 = 88 feet.