Write the equation and solve the problem. The length of a rectangle is four less than twice the width. If the perimeter is 34, find the length and the width.

The formula of a perimeter of a rectangle:

P = 2 (l + w)

We have P = 34 and l = 2w - 4.

Substitute:

2 (2w - 4 + w) = 34

2 (3w - 4) = 34 use distributive property

(2) (3w) + (2) (-4) = 34

6w - 8 = 34 add 8 to both sides

6w = 42 divide both sides by 6

w = 7

l = 2w - 4 → l = 2 (7) - 4 = 14 - 4 = 10

Answer: the length = 10 and the width = 7.