Question

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

Answer 1

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.

Answer 2

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.