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

Answer:

The width is:

• width = 4.7 feet

The length is:

• length = 11.3 feet

Step-by-step 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

$\frac{6w}{6}=\frac{28}{6}$

$w=\frac{14}{3}$

Hence, the width is:

$w=\frac{14}{3}$

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