If the length of a rectangle is twice its width, w, write an expression to represent the perimeter of the rectangle. If the perimeter of the rectangle is 72 inches, what is the length and width of the rectangle?

P = 2L + 2W

72 = 2(2W) + 2W

72 = 6W
12 = W

To write an expression to represent the perimeter of a rectangle, we need to understand the formula for the perimeter of a rectangle. The perimeter is the sum of all the sides of the rectangle.

In this case, the rectangle has a length that is twice its width. Let's call the width of the rectangle "w". According to the problem, the length would then be "2w" since it is twice the width.

The formula for the perimeter of a rectangle is 2 * length + 2 * width.

So, the expression to represent the perimeter of this rectangle would be: 2 * (2w) + 2 * w.

Now, given that the perimeter of the rectangle is 72 inches, we can set up the equation and solve for the width and length.

2 * (2w) + 2 * w = 72

Simplifying the equation, we have:

4w + 2w = 72
6w = 72
w = 12

Therefore, the width of the rectangle is 12 inches. To find the length, we can substitute this value back into the formula for the length: length = 2w.

length = 2 * 12 = 24

So, the length of the rectangle is 24 inches and the width is 12 inches.