the perimeter of a rectangular window is 28 feet. the width of the window is 4 feet more than the length. what are the dimensions of the window?

Question

how do you find the dimensions with out knowing anything but the perimeter ?

Answer 1

Perimeter of the window = 28 feet

 

let the length of the window be x

so the width of the window = 4 more than length = x+4

 

perimeter = length of boundary 

          28  = length + breadth + length + breadth 

          28  = x + (x+4) + x+ (x+4) 

          28  = x+ x+ 4+ x+ x+ 4

          28  = 4x + 8

        28-8 = 4x

          20  = 4x

        20/4 = x

           5   = x

 

so the  length of the window = x = 5 feet

  and the width of the window = x+4 = 5+4 = 9 feet 

Answer 2

The perimeter of any rectangle is the sum of twice the width and twice the length.

 

Perimeter = 2(width) + 2(width)

 

 

Let length = x

Let width = x + 4

Perimeter = 28

 

 

Set up an equation using the variables and formula for perimeter.

 

2x + 2(x + 4) = 28

 

 

Solve for x from this equation.

 

2x + 2x + 8 = 28

4x + 8 = 28

4x = 20

  x = 5

 

 

Substitute this value of x into the variables to find your dimensions.

 

 

Answer 3

Let x=the length; then  x+4 = width 

The perimeter of a rectangle is 2w + 2l where w= width and l=length; so we have the perimeter in this case:

 2x + 2(x+4)= 28

4x+8=28

4x=20

x=5

So the dimensions:, the length is 5 ft and the width is 9 ft.  

Check the solution 2(9) + 2(5)=28. Correct!