The length of a rectangle is 4 cm less than twice it's width. It's perimeter is 40 cm. Find its length and width

Question

The length of the rectangle is 4 cm less than twice it's width. It's perimeter is 40 cm. What is the length and width. 

Answer 1

Let l = length

w= width

 

2w -2 = l ..........  ..... Eq 1

 

Perimeter = l+w+l+w = 2l +2w = 40........ Eq 2

 

fron Eq 1  l = 2w -2

 

Substituting in Eq 2

 

2( 2w-2) +2w = 40

6w  = 44

 w = 7.33

 from Eq 1       l =  2x7.33 - 2 = 12.66 cm

 

 

Answer 2

Let's assume that the width of the rectangle is w. The length is then 2w - 4 (since the problem states that the length is 4cm than twice the width). 

 

The formula for the perimeter of a rectangle is P = L + L + W + W or P = 2L + 2W

 

So, 40 = 2(2w-4) + 2w

      40 = 4w -8 + 2w

      40 = 6w - 8 

   40 + 8 = 6w

     48 = 6w

      8 = w

 

The width is 8. The length is 2w - 4 = 2(8) - 4 = 12

 

To double check: 2W + 2L = 2(8) + 2 (12) = 16 + 24 = 40 

Answer 3

Let the width of rectangle = w

 

Length of rectangle (l) = 2*w - 4

 

Perimeter = 2*l + 2*w = 2(l+w)

 

2(2w -4 +w) = 40

 

3w - 4 =20

 

width = 8cm

 

length = 12cm