Final answer:
The function that models the perimeter P of a rectangle with an area of 13 m² in terms of the length x of one of its sides is P(x) = 2x + (26/x).
Step-by-step explanation:
You wish to find a function that models the perimeter P of a rectangle in terms of one of its sides, x, given that the area A of the rectangle is 13 m². First, we can express the area of the rectangle as A = x × y, where x is the length and y is the width.
Since the area A is 13 m², we have 13 = x × y. To find y as a function of x, we rearrange this equation to y = 13/x.
The perimeter P of a rectangle is given by P = 2 × (length + width) which can be written as P = 2x + 2y. Substituting the expression for y into the perimeter formula gives us P(x) = 2x + 2(13/x). This is the function that models the perimeter P in terms of the side length x.
Given that the area is 13 m², we can express it in terms of the length x and the width (13 = x * width). Rearranging this equation, we get width = 13 / x. Substituting this value of width into the perimeter formula, we have P = 2 * (x + 13 / x).
Therefore, the function that models the perimeter P in terms of the length x of one side of the rectangle is P(x) = 2 * (x + 13 / x).
So, P(x) = 2x + (26/x) would be the function in terms of x.