The equation is 2(3x + 9) = 54
The length is 21 m and the width is 6 m
Step-by-step explanation:
Joe is planning a rectangular garden for spring and he needs to fence it to keep the rabbits out
- He has 54 m of fencing to go around the perimeter of the garden
- He wants the length of the garden to be 9 m more than twice the width
We need to set up an equation to solve it and find the length and the width
Assume that the width of the garden is x meters
∵ The width of the garden is x meters
∵ The length of the garden has to be 9 m more than twice the width
- Multiply x by 2 and then add 9 to find the length
∴ The length = 2x + 9
∵ The perimeter of a rectangle = 2(length + width)
∵ Length = 2x + 9
∵ Width = x
∴ The perimeter of the garden = 2(2x + 9 + x)
- Add like terms
∴ The perimeter of the garden = 2(3x + 9)
∵ The length of the fence = 54 m
∵ The length of the fence is the perimeter of the garden
- Equate the perimeter of the garden by 54
∴ 2(3x + 9) = 54
- Subtract 18 from both sides
∴ 6x = 36
- Divide both sides by 6
∴ x = 6
∵ x represents the width of the garden
∴ The width of the garden is 6 meters
∵ 2x + 9 represents the length of the garden
∴ The length of the garden = 2(6) + 9 = 12 + 9 = 21 meters
The equation is 2(3x + 9) = 54
The length is 21 m and the width is 6 m
Learn more:
You can learn more about solving linear equations in brainly.com/question/13168205
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