Question

A landscaper has 72 ft. of fencing to put around a rectangular garden. If the length is 3 times the width, what are the dimensions of the garden?

A. Width = 6 ft, Length = 18 ft

B. Width = 8 ft, Length = 24 ft

C. Width = 9 ft, Length = 27 ft

D. Width = 12 ft, Length = 36 ft

Answer 1

The correct dimensions of the garden are a width of 9 ft and a length of 27 ft, as determined by using the perimeter formula and the relationship between the length and width.

Step-by-step explanation:

The student needs to find the dimensions of a rectangular garden using the given total fencing length and the relationship between the garden's length and width. To solve for the dimensions, we use the perimeter formula for a rectangle, which is P = 2l + 2w (where P is the perimeter, l is the length, and w is the width).

The problem states that the length (l) is three times the width (w), so we can express this as l = 3w. We also know that the total perimeter is 72 ft. Plugging in the expressions into the perimeter formula, we get 72 = 2(3w) + 2w, which simplifies to 72 = 8w. Dividing 72 by 8, we find that w = 9 ft. Therefore, the length is l = 3w = 3 * 9 = 27 ft. Consequently, the dimensions of the garden are Width = 9 ft and Length = 27 ft, which corresponds to option C.