The length of a rectangle is three times its width. If the area of the rectangle is 108 in2 , find its perimeter.

Question

The length of a rectangle is three times its width.
If the area of the rectangle is
108in2
, find its perimeter.

Answer 1

Let w = width

 

Then 3w = length

 

A= LW

 

108 = (3w)(w)

 

108 = 3w²

 

36 = w²

 

6 = w   18 = length  Perimeter = 2(6) + 2(18) = 48 in

Answer 2

The area of a rectangle is length times width.  The perimeter is the sum of twice the width and twice the length.

 

Let width = x

Let length = 3x

 

Using these variables, we can write an equation that represents the area.

 

x(3x) = 108

 

3x² = 108

 

 

Solve the equation for x.

 

x² = 36

 

x = 6

 

The width is 6in.  The width is then 18in.

 

 

Using these values of width and length that we just found, we can get the perimeter.

 

Perimeter = 2(6) + 2(18)

 

Perimeter = 2(6 + 18)

 

Perimeter = 2(24)

 

Perimeter = 48 in