Final answer:
The area of the rectangle is found by first determining its length and width using the perimeter and given relationship between them, then multiplying the length by the width. The calculated area of the rectangle is 207 square inches.
Step-by-step explanation:
The student is asked to calculate the area of a rectangle with a given perimeter and a relationship between its length and width. First, we use the perimeter to determine the length and width of the rectangle. With the perimeter being 64 inches and the length being 5 more than twice the width (L = 2W + 5), we can set up the equation for perimeter (P = 2L + 2W) and solve for W, then find L using the given relationship. Once we have the length and width, we can calculate the area (A = L × W).
Step-by-Step Solution:
- Use the perimeter formula: P = 2L + 2W, where P is 64 inches.
- Substitute L with (2W + 5) in the perimeter formula: 64 = 2(2W + 5) + 2W.
- Solve for W: 64 = 4W + 10 + 2W; 64 = 6W + 10; W = 9 inches.
- Find L using the relationship L = 2W + 5: L = 2(9) + 5; L = 23 inches.
- Calculate the area using A = L × W: A = 23 × 9; A = 207 square inches.
The area of the rectangle is 207 square inches.