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 length of the garden will be about 6 feet. Is your dad's estimate reasonable?
To determine if your dad's estimate is reasonable, let's calculate the actual dimensions of the garden based on the given information.
Let's assume the width of the garden is x feet. Then, according to the problem, the length of the garden is 2½ feet longer than the width, so it would be x + 2½ feet.
The perimeter of a rectangle is given by the formula P = 2(length + width). We are given that the total fencing available is 20 feet, so 20 = 2(x + 2½ + x).
Simplifying the equation, we get 20 = 4x + 5. Subtracting 5 from both sides, we have 15 = 4x. Dividing both sides by 4, we find that x = 3.75.
Therefore, according to the calculations, the width of the garden is 3.75 feet and the length is 3.75 + 2½ = 6.25 feet.
Comparing this with your dad's estimate of 6 feet, it seems quite reasonable as it is only 0.25 feet (or 3 inches) longer than his estimate.