Kareem has 28ft of fencing. He has to decide on the length and the width of his garden. Which of the following garden sizes would use exactly 28 ft of fence?
Which following?
To determine the garden size that would use exactly 28 ft of fence, we need to consider the perimeter of the garden.
The perimeter of a rectangular garden is calculated by adding twice the length to twice the width:
Perimeter = 2 * Length + 2 * Width.
We can now try different combinations of lengths and widths to find the one that uses exactly 28 ft of fence.
1. Let's start with a length of 10 ft and a width of 4 ft:
Perimeter = 2 * 10 + 2 * 4 = 20 + 8 = 28 ft.
So, a garden with a length of 10 ft and a width of 4 ft would use exactly 28 ft of fence.
2. Now, let's try a different combination. With a length of 8 ft and a width of 6 ft:
Perimeter = 2 * 8 + 2 * 6 = 16 + 12 = 28 ft.
So, a garden with a length of 8 ft and a width of 6 ft would also use exactly 28 ft of fence.
Therefore, the garden sizes that would use exactly 28 ft of fence are:
- A garden with a length of 10 ft and a width of 4 ft.
- A garden with a length of 8 ft and a width of 6 ft.
To determine which garden size would use exactly 28 feet of fence, we can set up an equation using the perimeter formula for a rectangle.
Let's assume the length of the garden is L feet, and the width is W feet.
The perimeter formula for a rectangle is: Perimeter = 2 * (Length + Width)
We know that the perimeter of the garden (fence length) is 28 feet, so we can write the equation:
28 = 2 * (L + W)
Simplifying this equation, we get:
14 = L + W
Now, we need to find whole number values for L and W that satisfy this equation.
We can list all possible pairs of whole numbers that add up to 14:
(1, 13), (2, 12), (3, 11), (4, 10), (5, 9), (6, 8), (7, 7)
The pairs (7, 7) is the only one that satisfies the equation, as both numbers are the same.
Therefore, the garden size that would use exactly 28 feet of fence is a square garden with a length and width of 7 feet.