Your dad is designing a new rectangular garden for your backyard. He has 26 feet of fencing to go around the garden. He wants the length of the garden to be 3 1/2 feet longer than the width. How long 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 3 1/2 feet longer than the width, which will be x + 3 1/2 feet.
The perimeter of a rectangle can be calculated by adding the length of all its sides. In this case, the perimeter is 2 times the length plus 2 times the width.
So, according to the problem, the perimeter is 2(x + 3 1/2) + 2(x) = 26 feet.
Simplifying the equation, we get 2x + 7 + 2x = 26, or 4x + 7 = 26.
Subtracting 7 from both sides of the equation, we get 4x = 19.
Dividing both sides of the equation by 4, we get x = 19/4 = 4.75 feet.
Therefore, the width of the garden is 4.75 feet and the length is 4.75 + 3 1/2 = 8.25 feet. My dad should make the garden 8.25 feet long.