The perimeter of a rectangle garden is 104 ft. The length of the garden is 8 less than twice the width. What are the dimensions of the garden.
2 L + 2 w = 104
so L + w = 52 and L = (52-w)
L + 8 = 2 w
52 - w + 8 = 2 w
w = 30
L = 52 - 30 = 22
To find the dimensions of the garden, we need to set up a system of equations based on the given information.
Let's denote the width of the garden as 'w' and the length as 'l'.
From the given information, we have two equations:
1. The perimeter of a rectangle is given by the formula: P = 2(l + w)
Plugging in the given perimeter value of 104 ft, we get: 104 = 2(l + w)
2. The length of the garden is 8 less than twice the width: l = 2w - 8
Now, we can solve this system of equations.
Let's substitute equation 2 into equation 1:
104 = 2(l + w)
104 = 2((2w - 8) + w)
104 = 2(3w - 8)
104 = 6w - 16
120 = 6w
w = 20
Now, substitute the value of w back into equation 2 to find l:
l = 2w - 8
l = 2(20) - 8
l = 40 - 8
l = 32
Therefore, the dimensions of the rectangle garden are width = 20 ft and length = 32 ft.