The length of a rectangle is 6cm longer than the width. If the length is increased by 9cm and the width by 5cm, the perimeter will be 160cm. find the dimensions of the original rectangle.

x = width

x + 6 = length {length is 6 longer than width}

x + 5 = new width {width is increased by 5}

x + 15 = new length {length is increased by 9}

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

2(x + 5) + 2(x + 15) = 160 {perimeter is 2(width) + 2(length)}

2x + 10 + 2x + 30 = 160 {used distributive property}

4x + 40 = 160 {combined like terms}

4x = 120 {subtracted 40 from both sides}

x = 30 {divided both sides by 4}

x + 6 = 36 {substituted 32.5, in for x, into x + 6}

original

**width = 30 cm**

original

**length = 36 cm**

*© Algebra House*