The length of a rectangular garden is 4 ft less than 3 times its width. If the perimeter of the garden is 40 ft, find the dimensions of the garden.
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Let's start by assigning variables to represent the dimensions of the garden. Let's use L for length and W for width.
According to the problem, the length of the garden is 4 feet less than 3 times its width:
L = 3W - 4
We are also given that the perimeter of the garden is 40 feet. The formula for the perimeter of a rectangle is P = 2L + 2W, so we can set up the following equation:
2L + 2W = 40
Now, we can substitute the expression for L from the first equation into the second equation:
2(3W - 4) + 2W = 40
Simplifying this equation:
6W - 8 + 2W = 40
Combining like terms:
8W - 8 = 40
Adding 8 to both sides:
8W = 48
Dividing both sides by 8:
W = 6
Now that we have the value of W, we can substitute it back into the first equation to find the value of L:
L = 3(6) - 4
L = 18 - 4
L = 14
Therefore, the dimensions of the garden are 14 ft for length and 6 ft for width.