Final answer:
To find the perimeter of the rectangle, we need to determine its dimensions. Let's say the width of the rectangle is x inches. According to the problem, the length of the rectangle is 3 inches longer than its width, so the length is x + 3 inches. The area of the rectangle can be calculated by multiplying the width and length, so we have x(x + 3) square inches. The perimeter of the rectangle can be found by adding all four sides, which is 2x + 2(x + 3) inches.
Step-by-step explanation:
To find the perimeter of the rectangle, we need to determine its dimensions. Let's say the width of the rectangle is x inches. According to the problem, the length of the rectangle is 3 inches longer than its width, so the length is x + 3 inches. The area of the rectangle can be calculated by multiplying the width and length, so we have x(x + 3) square inches. The perimeter of the rectangle can be found by adding all four sides, which is 2x + 2(x + 3) inches.
The problem states that the area exceeds the perimeter by 24. So, we have the equation x(x + 3) = 2x + 2(x + 3) + 24. Simplifying this equation, we get x^2 + 3x = 4x + 6 + 24. Combining like terms, we have x^2 - x - 30 = 0.
Factoring this quadratic equation, we get (x - 6)(x + 5) = 0. So, x = 6 (since a negative width doesn't make sense in this context). Therefore, the width of the rectangle is 6 inches, and the length is 6 + 3 = 9 inches. The perimeter of the rectangle is 2(6) + 2(9) = 12 + 18 = 30 inches. Therefore, the answer is C) 30 inches.