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 wide should he make the garden?
Let the width of the garden be x feet.
Therefore, the length of the garden is x + 3 1/2 = x + 7/2 feet.
The perimeter of the rectangular garden is the sum of all four sides, which is given by 2(width) + 2(length).
The perimeter is given as 26 feet, so we can set up the equation:
2x + 2(x + 7/2) = 26
We can simplify the equation by distributing and combining like terms:
2x + 2x + 7 = 26
4x + 7 = 26
Next, we can isolate the variable x by subtracting 7 from both sides of the equation:
4x + 7 - 7 = 26 - 7
4x = 19
Finally, we can solve for x by dividing both sides of the equation by 4:
4x/4 = 19/4
x = 4.75 feet
Therefore, your dad should make the garden 4.75 feet wide.