Final answer:
The dimensions of the rectangle with a perimeter of 60 inches and with the length being 7 inches more than the width are 18.5 inches (length) and 11.5 inches (width).
Step-by-step explanation:
The question given is asking us to find the dimensions of a rectangle, knowing the relationship between the length and width and its perimeter. Let's denote the width of the rectangle as w inches. According to the problem, the length is 7 inches more than its width, so it can be represented as w + 7 inches. The perimeter of a rectangle is the sum of all its sides, that is, 2 × length + 2 × width. Since the perimeter is 60 inches, the equation to represent this situation would be 2(w + 7) + 2w = 60.
We can solve this equation to find w. First, expand the equation: 2w + 14 + 2w = 60. Combine like terms: 4w + 14 = 60. Subtract 14 from both sides: 4w = 46. Lastly, divide both sides by 4 to get w: w = 11.5. Now that we know the width, we can determine the length by adding 7: Length = 11.5 + 7 = 18.5 inches. Therefore, the dimensions of the rectangle are 18.5 inches by 11.5 inches.