The perimeter of dana's rectangular garden is 61 feet. the length of her garden is 5 feet more than twice the width. create an equation or equations that can be used to determine the length and width of the garden. be sure to define your variables. what is the length and width of the garden? show all your work. enter your definition of variables, equation( s), answers, and work in the box provided.

The length of the garden is 22 feet and the width of the garden is 8.5 feet and this can be determined by forming the linear equation.

Given :

The following steps can be used in order to determine the length and width of the garden:

Step 1 - Let 'L' be the length of the garden and 'w' is the width of the garden.

Step 2 - The linear equation that represents the length of Dana's garden is 5 feet more than twice the width is given by:

L = 5 + 2w    --- (1)

Step 3 - The linear equation that represents the perimeter of Dana's rectangular garden is 61 feet is given by:

2L + 2w = 61 --- (2)

Step 4 - Substitute the value of L in equation (2).

2(5 + 2w) + 2w = 61

Simplify the above equation.

10 + 4w + 2w = 61

6w = 51

w = 8.5 feet

Step 5 - Substitute the value of 'w' in equation (1).

L = 2(8.5) + 5

L = 17 + 5

L = 22 feet

So, the length of the garden is 22 feet and the width of the garden is 8.5 feet.

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l = 2w + 5

2l + 2w = 61

2(2w + 5) + 2w = 61

4w + 10 + 2w = 61

6w = 51

w = 51/6

w = 8.5

l = 22