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 2½ feet longer than the width. Your dad estimates that the width of the garden will be about 2 feet. Is your dad's estimate reasonable?
To determine if your dad's estimate is reasonable, we can calculate the length of the garden using the given information.
Let's assume the width of the garden is w feet. According to the problem, the length of the garden is 2½ feet longer than the width, so the length is (w + 2½) feet.
The perimeter of a rectangular garden is given by the formula P = 2w + 2l, where P is the perimeter, w is the width, and l is the length.
Given that the perimeter is 20 feet, we can set up the equation:
20 = 2w + 2(w + 2½)
Simplifying the equation:
20 = 2w + 2w + 5
Combining like terms:
20 = 4w + 5
Subtracting 5 from both sides of the equation:
15 = 4w
Dividing both sides of the equation by 4:
w = 3.75
Therefore, your dad's estimate of 2 feet for the width of the garden is not reasonable, since the width is actually 3.75 feet.