What are the dimensions of the rectangular rug?

Question

The perimeter of a rectangular rug is 32 ft.  The length is 2ft longer than the width.  What are the dimensions of the rug?

Answer 1

Let L = the length of the rug and W = the width

 

The length of the perimeter is the total distance around the rug = 2L + 2W = 32

 

Now the Length is 2 feet more than the width; that is L = W + 2.  Let's substitute W + 2 for L in the perimeter equation

 

32 = 2L + 2W = 2(W + 2) + 2W = 2W + 4 + 2W = 4W + 4

 

32 = 4W + 4

 

28 = 4W

 

Now solve for the width, W.  Once you have W, get the Length by using the formula L = W + 2.  To check, plug your answers for L and W into the perimeter formula and be sure it adds up to 32

 

Answer 2

A similar problem:

 

The perimeter of a rectangular rug is 36 ft. The length is 3 ft longer than the width. What are the dimensions of the rug?

 

p = 36 = 2x + 2y

 

y = x + 3

 

36 = 2x + 2(x + 3)

 

36 = 2x + 2x + 6

 

36 – 6 = 4x

 

4x = 30

 

x = 30/4 = 15/2 = 7.5 feet

 

y = 7.5 + 3 = 10.5 feet

Answer 3

Hi Mary,

 

The perimeter of the rectangular rug=2(l+w)=32ft.

 

Let the width be w

 

The length is 2 ft.longer than width

 

Length, l=w+2

 

2(l+w)=32

 

2(w+2+w)=32

 

2(2w+2)=32

 

4w+4=32

 

4w=28

 

4w/4=28/4

 

w=7

 

The width of the rug=7ft.

 

and the length of the rug=2+w=2+7=9ft.