Frank the Fencemaker needs to fence in a rectangular yard. He fence in three of four sides of the yard. The unfenced side of the yard is 40 feet long. The yard has an area of 280 square feet. What is the length , in feet, of the fence that Frank installs?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the problem
Frank needs to fence three sides of a rectangular yard, with one side left unfenced. The length of the unfenced side is given as 40 feet, and the area of the yard is 280 square feet.

### Step 2: Set up the rectangle
Let’s denote the length of the yard as \( L \) and the width (or breadth) as \( W \). According to the problem:
- The unfenced side (length) is \( L = 40 \) feet.
- The area of the rectangle is given by the formula:
\[ \text{Area} = L \times W \]

### Step 3: Substitute the known values into the area formula
We know the area is 280 square feet, so we can set up the equation:
\[ 40 \times W = 280 \]

### Step 4: Solve for the width \( W \)
To find \( W \), we divide both sides of the equation by 40:
\[ W = \frac{280}{40} = 7 \text{ feet} \]

### Step 5: Calculate the total length of the fence
Frank fences three sides of the rectangle. The sides he fences are:
- One length of 40 feet
- Two widths of 7 feet each

The total length of the fence \( L_f \) can be calculated as:
\[ L_f = 40 + 7 + 7 = 54 \text{ feet} \]

### Step 6: Conclusion
Thus, the total length of the fence that Frank installs is 54 feet.

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