If the length of a rectangle is 7 more than the width of the rectangle and the area is 60sq.ft, find the perimeter of the rectangle.

x = width

x + 7 = length{length is 7 more than width}

x(x + 7) = 60 {area of a rectangle is width x length}

x² + 7x = 60 {used distributive property}

x² + 7x - 60 = 0 {subtracted 60 from both sides}

(x + 12)(x - 5) = 0 {factored into two binomials}

x + 12 = 0 or x - 5 = 0 {set each factor equal to 0}

x = -12 or x = 5 {subtracted 12 and added 5 respectively}

x = 5 {width of a rectangle cannot be negative}

x + 7 = 12 {substituted 5, in for x, into x + 7}

width = 5 ft and length = 12 ft

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

= 2(5) + 2(12) {substituted width and length into perimeter formula}

= 10 + 24 {multiplied}

**Perimeter = 34 ft**{added 10 and 24}