Final answer:
To find the area of a garden with given perimeter and length-width relationship, equations for a rectangle's perimeter and its length in terms of width are used. Upon simplifying the equations, the width and length are found, and subsequently, the area is calculated by multiplying these dimensions.
Step-by-step explanation:
The student asks for help to find the area of a rectangular garden, where the length is 4 feet longer than the width and the perimeter is 192 feet. We start with two equations based on the information given: the perimeter (P) formula for a rectangle P = 2(length + width) and the relationship between the length (L) and width (W), which is L = W + 4. With a known perimeter of 192 feet, we substitute L with W + 4 into the perimeter equation to get 2(W + 4 + W) = 192, which simplifies to 2W + 8 + 2W = 192 and further to 4W + 8 = 192. Solving for W gives us W = 46 feet. Subsequently, L = W + 4 = 50 feet. The area (A) of the rectangle is found using A = length × width, which in this case is A = 50 × 46 = 2300 square feet.