Final answer:
The area of the rectangle garden with a length that is 4 feet longer than the width and a perimeter of 32 feet is 60 square feet.
Step-by-step explanation:
The question pertains to finding the area of a rectangle garden when the perimeter is given, and the relationship between the lengths of its sides is known.
Let's define the width of the garden as w feet. It is given that the length of the rectangle garden is 4 feet longer than the width, so the length l can be represented as w + 4 feet.
The perimeter of a rectangle is calculated as 2×(length + width). Since the perimeter is 32 feet, we can set up the equation 2×(w + w + 4) = 32. Simplifying, we have 4×w + 8 = 32, and further simplifying, we find w = 6 feet.
Knowing the width, we can find the length: l = w + 4 = 10 feet. The area of a rectangle is calculated as length × width, so the area of this garden is 10 feet × 6 feet = 60 square feet.