Your dad is designing a new rectangular garden for your backyard. He has 20 feet of fencing to go around the garden. He wants the length of the garden to be 2 1/2 feet longer than the width. How wide should he make the garden?
Let's assume the width of the garden is x feet.
According to the problem, the length of the garden is 2 1/2 feet longer than the width, so it will be (x + 2 1/2) feet.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is 20 feet, so we can set up the equation.
20 = 2((x + 2 1/2) + x)
Now we can simplify the equation.
20 = 2(2x + 2 1/2)
20 = 4x + 5
Subtracting 5 from both sides of the equation, we get:
15 = 4x
Dividing both sides by 4, we get:
x = 3.75
Therefore, your dad should make the width of the garden 3.75 feet.