Question

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

• A. 34
• B. 40
• C. 68
• D. 88
• E. 90

Hint:

In problems where "one side is left uncovered," always visualize the rectangle to ensure you are adding the correct combination of sides (either $L + 2W$ or $2L + W$).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given a rectangular field with a known area. It needs to be fenced on only three sides. One side, which measures 20 feet, is left open. We need to find the total length of the fencing required.
Step 2: Key Formula or Approach:
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \] The total fencing will be the sum of the lengths of the three sides that are fenced.
Step 3: Detailed Explanation:
Let the length of the rectangular field be \(L\) and the width be \(W\).
The area of the field is given as 680 sq ft.
\[ L \times W = 680 \] We are told that one side measuring 20 feet is left uncovered. This means one of the dimensions (either Length or Width) is 20 feet. Let's assume this side is the Length, so \(L = 20\) feet.
Now we can find the other dimension, the Width (\(W\)):
\[ 20 \times W = 680 \] \[ W = \frac{680}{20} \] \[ W = 34 \text{ feet} \] So, the dimensions of the rectangular field are 20 feet and 34 feet.
The fencing is on three sides, leaving one 20-foot side open. This means the fence will cover the other 20-foot side and the two 34-foot sides.
The total length of the fencing required is the sum of these three sides:
\[ \text{Fencing} = (\text{One side of length } L) + (\text{Two sides of length } W) \] \[ \text{Fencing} = 20 + 34 + 34 \] \[ \text{Fencing} = 20 + 68 \] \[ \text{Fencing} = 88 \text{ feet} \] Alternatively, if the unfenced side was one of the 34-foot sides, the fencing would be \(34 + 20 + 20 = 74\) feet, which is not among the options. Therefore, the first scenario is correct.
Step 4: Final Answer:
The total length of fencing required is 88 feet.