Question

The length of a rectangle is twice as great as its width. When both the width and length are increased by 5 inches, the new rectangle has perimeter of 80 inches. Show an equation to find the length and width of the original rectangle. Solve the equation and give the original length and width.

Answer 1

Original rectangle

Length = 20 inches

Width = 10 inches

Explanation:

Let

Original rectangle

Width = x

Length = 2x

When both the width and length are increased by 5 inches, the new rectangle has perimeter of 80 inches

New rectangle

Width = x + 5

Length = 2x + 5

Perimeter = 80 inches

Perimeter of a rectangle = 2(length + Width)

80 = 2{(x+5) + (2x+5)}

80 = 2( x + 5 + 2x + 5)

80 = 2(3x + 10)

80 = 6x + 20

80 - 20 = 6x

60 = 6x

x = 60 / 6

= 10

x = 10 inches

The length and width of the original rectangle

Width = x

= 10 inches

Length = 2x

= 2(10)

= 20 inches