Question

The perimeter of a child's rectangular sandbox is 18 feet. If the length of the sandbox is one foot longer than the width, what equation can be used to find the length and width of the sandbox? Be sure to label your variable(s).

a) (2x + 2(x + 1) = 18)
b) (2x + 2x = 18)
c) (2(x + 1) + 2x = 18)
d) (x + (x + 1) = 18)

Answer 1

The correct equation to find the dimensions of the sandbox, where the length is one foot longer than the width, is (2x + 2(x + 1) = 18), representing the perimeter of a rectangle. The width is represented by x, and the length by x + 1.

Step-by-step explanation:

To find the length and width of a child's rectangular sandbox with a perimeter of 18 feet, where the length is one foot longer than the width, you would use the following equation:

(2x + 2(x + 1) = 18)

Here's why: let's define the width of the sandbox as 'x'. Since we know the length is one foot longer, the length would be 'x + 1'. A rectangle's perimeter is calculated by the formula P = 2l + 2w where l is length and w is width. Plugging our expressions for length and width into the perimeter formula, we get:

2x (for the width) plus 2 times (x + 1) (for the length). Simplified, this gives us the correct equation a).