Word problem involving perimeter

The perimeter of a rectangle is 74 inches. Find the dimensions if the length is 7 inches greater than twice the width.

x = width
2x + 7 = length {the length is 7 greater than the twice the width}

Perimeter of a rectangle is 2(width) + 2(length)

2x + 2(2x + 7) = 74 {perimeter is 2(width) + 2(length)}
2x + 4x + 14 = 74 {used distributive property}
6x + 14 = 74 {combined like terms}
6x = 60 {subtracted 14 from each side}
x = 10 {divided each side by 6}
2x + 7 = 27 {substituted 10, in for x, into 2x + 7}

width is 10 inches
length is 27 inches

- Algebra House