The length of a rectangle is twice its width. If the perimeter of the rectangle is 42 inches, find its length and width.

The perimeter of a rectangle (or any figure, for that matter) is the sum of the lengths of its sides.

P = L + W + L + W

P = 2 (L + W)

Your problem statement tells you L = 2W, so you can make the substitution of given information to get

P = 2 (2W + W)

P = 6W

42 in = 6W

(42 in) / 6 = W = 7 in

The length is twice that, so is 2 * (7 in) = 14 in.

The length is 14 in.

The width is 7 in.