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Answer :
Answer:
3w = 54
Step-by-step explanation:
Let the width of the garden be w
Length = 2w + 6
Perimeter = 120 feet
2* (length + Width) = 120
2*(2w + 6 + w) = 120
3w + 6 = 120/2
3w + 6 = 60
3w = 60 - 6
3w = 54
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Final answer:
Given the problem's information, we form an equation for the perimeter of the rectangle in terms of width. Upon simplifying, we find that the width of the garden measures 18 feet.
Explanation:
This problem can be approached using algebra principles applied to geometry. We know that the perimeter of a rectangle is given by the formula P=2L+2W, where P is the perimeter, L is the length, and W is the width. The problem gives us the total perimeter as 120 feet, and tells us that the length is six feet more than twice the width. This can be expressed algebraically as L=2W+6.
Substituting the value of L from the second equation into the first gives us a new equation, 120=2(2W+6)+2W, for the perimeter in terms of W. Simplifying, we get 120=6W+12, and subtracting 12 from both sides gives the final equation W=18, which represents the width of the garden in feet.
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