Final answer:
The area of the garden is calculated by first determining the width using the given perimeter of the fencing, and then using the relationship between the length and width. The width is found to be 10 feet, the length is 30 feet, and hence, the garden's area is 300 square feet.
Step-by-step explanation:
To find the area of the garden, we first need to establish the dimensions of the garden using the given perimeter of the fencing. Since the length of the garden lies along a patio wall and is not enclosed by the fencing, only three sides of the garden require fencing. Therefore, the perimeter of the fencing encloses two widths and one length of the garden, which can be expressed as 50 feet = 2W + L, where W is the width and L is the length. Given that the length is three times the width (L = 3W), we can substitute this into the perimeter equation to find the width.
Substituting L = 3W into the perimeter equation gives us: 50 = 2W + 3W, or 50 = 5W. By dividing both sides by 5, we find the width: W = 10 feet. Next, we calculate the length by multiplying the width by 3: L = 3W = 3 × 10 = 30 feet.
Now that we know the width and length of the garden, we can calculate the area by multiplying them together: Area = width × length = 10 feet × 30 feet = 300 square feet.
Therefore, the area of the garden is 300 square feet.