Final answer:
To find the area of the rectangle, we need to find the length and width using the given information. Then, we can use the formula for the area of a rectangle to calculate the area. The correct answer is 180 square inches.
Step-by-step explanation:
To find the area of the rectangle, we need to first calculate the length and width. The problem states that the width is 8 inches shorter than the length, so let's use variables to represent the length and width. Let's say the length is L inches and the width is L - 8 inches.
The perimeter of a rectangle is given by the formula P = 2(L + W), where P is the perimeter, L is the length, and W is the width. We are given that the perimeter is 56 inches, so we can substitute these values into the formula and solve for L.
56 = 2(L + (L - 8))
Simplifying the equation gives: 56 = 4L - 16
Adding 16 to both sides: 72 = 4L
Dividing both sides by 4 gives us: 18 = L
Now we can substitute the value of L back into the equation for the width: W = L - 8 = 18 - 8 = 10 inches.
The area of a rectangle is given by the formula A = L * W, substituting the values in gives us: A = 18 * 10 = 180 square inches. Therefore, the correct answer is 180 square inches.