Question

Roger is building a fence around a rectangular garden. The length of the garden is four times the width of the garden. Which represents the perimeter P of the garden as a function of the width w? Responses P(w) = 10w P(w) = 10w P(w) = 5w P(w) = 5w P(w) = 4w P(w) = 4w P(w) = 4w2

Answer 1

The perimeter P of the rectangular garden can be represented as the function P(w) = 10w, where w is the width of the garden.

Step-by-step explanation:

The perimeter P of a rectangular garden can be represented as a function of the width w by adding up all the sides of the garden. In this case, the length of the garden is four times the width, so we can write the equation as:

P(w) = 2w + 2(4w) = 2w + 8w = 10w

Therefore, the correct representation of the perimeter P of the garden as a function of the width w is P(w) = 10w.

Answer 2

The perimeter P of a rectangle with length four times its width w is represented by the function P(w) = 10w. This is derived using the formula for the perimeter of a rectangle and substituting the length with four times the width.

Step-by-step explanation:

The question revolves around finding the perimeter P of a rectangular garden as a function of its width w, given that the length of the garden is four times its width. To calculate the perimeter of a rectangle, the formula is P = 2l + 2w, where l is the length and w is the width. Since the length l is given as four times the width w, we can substitute l with 4w. Therefore, the formula for the perimeter becomes P(w) = 2(4w) + 2w, which simplifies to P(w) = 8w + 2w, and thus P(w) = 10w.