a playpen for a large dog has 12 panels. Each panel is 2 feet long. There are 3 different ways to arrange the panels so that each playpen has a different set of dimensions. Draw the shape of each possible playpen. Label the length and width of each playpen.

The drawing of the 3 different ways (obtained by writing the equation related to the information in the question) to arrange the panels that gives the 3 playpens different dimensions created with MS Word is attached.

What is a mathematical equation?

An equation is a mathematical (representation) of a statement that connects two expressions with an equals sign.

The number panels on the playpen = 12

Length of each panel = 2 feet long

The number of ways to arrange the panel = 3 ways

The number of panels on each side of the playpen can be found using the equation;

2·a + 2·b = 12

Where;

a and b are natural numbers (integers larger than zero)

a and b are the number of panels on a width and the adjacent length of the playpen

Therefore;

(2·a + 2·b)/2 = 12/2 = 6

2·(a + b)/2 = 6

a + b = 6

b = 6 - a

Fist configuration

When a = 1, b = 6 - 1 = 5

a = 1, b = 5

One configuration is therefore; the width of the playpen contains one panel and the length of the playpen contains 5 panels

Second configuration

When a = 2, b = 6 - 2 = 4

a = 2, b = 4

The second configuration is; There are two panels along the width of the playpen and four panels along the playpen's length.

Third configuration

When a = 3, b = 6 - 3 = 3

The third configuration is therefore; The width of the playpen has 3 panels and the length of the playpen has three panels.

Please find attached the shape of the three playpens based on the three possible arrangements created with MS Word

Learn more about writing mathematical equations here:

https://brainly.com/question/20475360

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