How Much Fencing Will Be Needed to Enclose a Rectangular Garden with an Area of 48 sq ft and a Length 2 ft Longer Than Its Width?
To find the amount of fencing needed, we must first determine the dimensions of the garden. Let's represent the width of the garden as "w" feet. Since the length is 2 feet longer than the width, the length will be "w + 2" feet.
The area of a rectangle is calculated by multiplying its length by its width. We are given that the area of the garden is 48 sq ft, so we have:
w * (w + 2) = 48
Expanding and simplifying the equation:
w² + 2w = 48
w² + 2w - 48 = 0
Using the quadratic formula, we solve for the value of "w":
w = (-2 ± √(2² + 4(1)(48))) / 2(1)
w = (-2 ± √(200)) / 2
w = (-2 ± 14.14) / 2
w = 6 or w = -8
Since the width cannot be negative, we disregard the solution w = -8. Therefore, the width of the garden is 6 feet.
Now that we know the width, we can calculate the length:
Length = w + 2 = 6 + 2 = 8 feet
The total amount of fencing needed is equal to the perimeter of the rectangular garden. The perimeter is calculated by adding the length of all four sides:
Perimeter = 2 * (Length + Width) = 2 * (8 + 6) = 2 * 14 = 28 feet
Therefore, the total amount of fencing needed to enclose the rectangular garden is 28 feet.
Related Questions:
- What is the formula for calculating the area of a rectangle?
Area = Length * Width - What is the formula for calculating the perimeter of a rectangle?
Perimeter = 2 * (Length + Width) - What is the width of the garden?
6 feet - What is the length of the garden?
8 feet - What is the total amount of fencing needed?
28 feet
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