Final answer:
To find the value of x and the dimensions of the rectangle, use the formula for the perimeter of a rectangle. Substitute the values from each option and see which one satisfies the equation. Option C is the correct answer, with x = 14.5, width = 16.5, and length = 39.5.
Step-by-step explanation:
To find the value of x and the dimensions of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2(length + width). In this case, the perimeter is given as 112, so we have 112 = 2(x + width). Since we're given three options, we can substitute the values from each option into the equation and see which one satisfies the equation.
Option A: x = 14.5, width = 39.5, length = 16.5: 112 = 2(14.5 + 39.5) = 2(54) = 108. This option does not satisfy the equation.
Option B: x = 15.4, width = 16.5, length = 20.6: 112 = 2(15.4 + 16.5) = 2(31.9) = 63.8. This option does not satisfy the equation.
Option C: x = 14.5, width = 16.5, length = 39.5: 112 = 2(14.5 + 16.5) = 2(31) = 62. This option satisfies the equation, so the correct answer is C. The value of x is 14.5, the width is 16.5, and the length is 39.5.