Final answer:
To find the dimensions of a rectangle with a perimeter of 68 ft and a length to width ratio of 9:8, use the equation 2(9x) + 2(8x) = 68, where x is the common multiplier for the length and width.
Step-by-step explanation:
The question is asking for the dimensions of the rectangle given its perimeter and the ratio of its length to width. Since the ratio of the length to the width is given as 9:8, let's represent the length as 9x and the width as 8x where x is the common multiplier. To find the dimensions of the rectangle, we need to set up an equation that relates the perimeter with these expressions.
The perimeter of a rectangle is calculated by adding twice the length plus twice the width, which is represented by the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we know that the perimeter (P) is 68 ft, so we substitute L with 9x and W with 8x to get the equation 2(9x) + 2(8x) = 68.
Therefore, the correct equation to use to solve this problem is Option D: 2(9x) + 2(8x) = 68.