A homeowner designs a rectangular garden such that the length is 20 feet more than twice the width. If 310 feet of picket fencing are to be used, find the length and width of the garden.
L=2W+20
310=2L+2W
Put the expression for L from the first equation, into the second, and solve for W. Then go back and solve for L
What do you mean?
310=2(2W+20)+2W
solve for W first.
To find the length and width of the garden, we can set up an equation based on the given information.
Let's assume that the width of the garden is "x" feet.
According to the problem, the length of the garden is 20 feet more than twice the width. So, the length can be represented as (2x + 20) feet.
Now, we know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
In this case, the perimeter is given as 310 feet. So, we can equate the equation:
310 = 2((2x + 20) + x)
Now, we need to solve this equation to find the value of "x" (width).
By simplifying the equation, we have:
310 = 2(3x + 20)
310 = 6x + 40
6x = 310 - 40
6x = 270
x = 270/6
x = 45
So, the width of the garden is 45 feet.
Now that we have found the value of the width, we can substitute it back into the expression for the length.
Length = 2x + 20
Length = 2(45) + 20
Length = 90 + 20
Length = 110
Therefore, the length of the garden is 110 feet and the width is 45 feet.