John made a rectangle pen for his dog using 28 feet of fencing. If the width of the pen is 2 feet more than one-half the length, what is the length and width of the pen?

The length of the pen is

6 feet

7 feet

8 feet

Okay, so you know that the perimeter of the pen is 28 feet. Now we need the separate side lengths.

P = 28 ft.

Length = x

Width = (1/2) x + 2

So now we can plug in the little equations of length and width into a perimeter formula:

2 (x) + 2 ((1/2) x + 2) = 28

Distribute the 2's and solve as needed.

2x + x + 4 = 28

3x + 4 = 28

3x = 24

x = 8

To find the width, just plug in 8 for x in our little equation:

(1/2) (8) + 2

= 6

So, the length is 8 feet and the width is 6 feet.

Let the length = x.

width = (x/2) + 2

28 feet of fencing implies the perimeter = 28

Perimeter = 2 * (L + W)

28 = 2 * (x + x/2 + 2)

28/2 = x + x/2 + 2

14 = 3x/2 + 2

14 - 2 = 3x/2

12 = 3x/2

3x/2 = 12

3x = 2*12

x = 2*12/3 = 8

Length of the pen, = x, x = 8

Length = 8 feet.