What are the length and width of a rectangular dog pen with a perimeter of 38 feet where the length is 2 feet less than twice the width? Write and solve a multi-step equation for the problem.

2L + 2W = 38

L - 2W = -2

3L = 36

L = 12

2W = L+2

2W = 14
W = 7

62feet what is the perimeter

To solve this problem, we can start by setting up equations based on the given information. Let's assume that the width of the dog pen is represented by the variable 'w' (in feet).

According to the problem, the length of the dog pen is 2 feet less than twice the width. Therefore, we can express the length as (2w - 2) feet.

The perimeter of a rectangle is given by the sum of all its sides. In this case, the perimeter is given as 38 feet. So, we can set up the equation:

Perimeter = 2(length + width)

Substituting the given values:

38 = 2((2w - 2) + w)

Simplifying the equation:

38 = 2(3w - 2)

Next, we need to distribute the 2 on the right side of the equation:

38 = 6w - 4

To isolate the variable term (6w), we can add 4 to both sides of the equation:

38 + 4 = 6w

42 = 6w

Finally, to solve for 'w', we can divide both sides of the equation by 6:

42/6 = 6w/6

7 = w

Therefore, the width of the rectangular dog pen is 7 feet.

To find the length, we can substitute the calculated width value (7) into the expression we derived earlier for the length:

Length = 2w - 2
= 2(7) - 2
= 14 - 2
= 12

Thus, the length of the dog pen is 12 feet.

Therefore, the rectangular dog pen has a width of 7 feet and a length of 12 feet.