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 Concept: c The field is a rectangle with length \(L\) and width \(W\). One side is already known (20 feet) and is not fenced. Since the area is given, we can find the dimensions of the other sides to calculate the total perimeter of the three fenced sides.
Step 2: Key Formula or Approach: 
1. Area of rectangle \(A = L \times W\). 
2. Fencing required \(P = \text{sum of the three fenced sides}\). 
Step 3: Detailed Explanation: 
1. We are given one side is 20 feet. Let's assume this is the width (\(W = 20\)).

2. Use the area to find the other dimension (\(L\)):

\[ 680 = 20 \times L \implies L = \frac{680}{20} = 34 \text{ feet} \] 3. The problem states that one side of 20 feet is left uncovered. This means the three sides being fenced are: - One side of 20 feet (the side opposite the uncovered side).

- Two sides of 34 feet each.

4. Total fencing required:

\[ P = 20 + 34 + 34 = 88 \text{ feet} \] 
Step 4: Final Answer: 
The total fencing required is 88 feet.