You have 540 feet of fencing to enclose a rectangular garden. You want the length of the garden to be 50 feet greater than the width. Find the length and width of the garden if you use all of the fencing.
P = 2L + 2W
540 = 2(W + 50) + 2W
540 = 4W + 100
440 = 4W
110 = W
x + (x+50) = 540/2 = 270
2 x + 50 = 270
2 x = 220
x = 110
x+50 = 160
To solve this problem, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
In this case, we are given that the perimeter of the garden is 540 feet. So, we have:
540 = 2L + 2W
We are also given that the length of the garden is 50 feet greater than the width. We can represent this by the equation L = W + 50.
Now, we can substitute L = W + 50 into the perimeter equation to solve for the width:
540 = 2(W + 50) + 2W
Simplifying this equation, we get:
540 = 2W + 100 + 2W
Combining like terms, we have:
540 = 4W + 100
Subtracting 100 from both sides, we have:
440 = 4W
Dividing both sides by 4, we get:
W = 110
Now that we know the width is 110 feet, we can substitute this value back into the equation L = W + 50 to find the length:
L = 110 + 50
L = 160
Therefore, the length of the garden is 160 feet, and the width is 110 feet.