Question

A rectangular garden is designed to be 8ft longer than it is wide. Let x represent the width of the garden. Write an expression for the perimeter in terms of the width x. Write the expression in simple terms.

Answer 1

To find the perimeter of a rectangular garden where the length is 8 feet longer than the width, represent the width with x, express the length as x + 8, and use the formula P = 2(length + width) to obtain the simplified expression for the perimeter: P = 4x + 16 feet.

Step-by-step explanation:

The question asks us to write an expression for the perimeter of a rectangular garden in terms of its width, given that the length is 8 feet longer than the width. The width is represented by x. Since the perimeter of a rectangle is given by the formula P = 2(length + width), we first express the length as x + 8 feet.

Substituting the width x and the length x + 8 into the perimeter formula, we get P = 2(x + (x + 8)). Simplifying this expression, we find the perimeter P = 2(2x + 8), which can be further simplified to P = 4x + 16 feet.