Question

you have 96 feet of fencing to enclose a rectangular pen for your dog. the pen should be three times long as it is wide. write and solve and equation find the dimensions of the pen.

Answer 1

Answer: Required equation :
`8w=96`

Dimensions of the pen:

Width = 12 feet and Length =36 feet.

Explanation:

Let w be the width of rectangular pen, then the length of the rectangular pen will be 3w.

We know that the perimeter of rectangle is given by "2length+2width".

Perimeter of rectangular pen = 2(3w)+2(w) =6w+2w=8w (1)

Given : You have 96 feet of fencing to enclose a rectangular pen for your dog.

i.e. Perimeter of rectangular pen = 96 feet (2)

From (1) and (2), we get

`8w=96\\\\\Rightarrow\ w=12` [Divide both sides by 8]

Thus, width = 12 feet and length = 3(12)=36 feet.

Answer 2

length = 36 ft; width = 12 ft

Explanation:

Let the width be x.

The length is 3x.

The perimeter is the sum of two lengths and two widths, and it equals 96 ft.

3x + 3x + x + x = 96

8x = 96

x = 12

Width = x = 12 ft

Length = 3x = 3(12 ft) = 36 ft