Question

The length of a rectangular dog run is 2 feet more than twice the width, w, and the perimeter of the dog run is 32 feet. Solve the equation

2w + 2(2w + 2) = 32 to find the width, w, of the dog run. Then find the length, 2w+2, of the dog run.

Answer 1

The width is:

• width = 4.7 feet

The length is:

• length = 11.3 feet

Explanation:

Given the equation

`2w\:+\:2\left(2w\:+\:2\right)\:=\:32`

`2w+4w+4=32` ∵
`a\left(b+c\right)=ab+ac`

Add similar elements: 2w+4w=6w

`6w+4=32`

subtract 4 from both sides

`6w+4-4=32-4`

`6w=28`

Divide both sides by 6

`(6w)/(6)=(28)/(6)`

`w=(14)/(3)`

Hence, the width is:

`w=(14)/(3)`

w = 4.7 feet

Therefore, the width is: 4.7 feet

As the length is:

2w+2 = 2(14/3)+2

= 28/3 + 2

= 34/3

= 11.3 feet

Therefore, the length is: 11.3 feet

SUMMARY:

The width is:

• width = 4.7 feet

The length is:

• length = 11.3 feet