The length of a rectangular Garden is 40 yards longer then double the width The perimeter of the garden is 470 yards. find length and width of the Garden.
L=2W+40
2W+2(2W+40=80
Am I starting off right?
yes,correct
Yes, you are starting off correctly by defining the length of the garden as 40 yards longer than double the width. The equation you have written is correct:
L = 2W + 40
where L represents the length and W represents the width.
To find the length and width of the garden, you need to use the second piece of information given, which is the perimeter of the garden being 470 yards. The formula for the perimeter, P, of a rectangle is:
P = 2L + 2W
Substitute the expression for L from the first equation into the perimeter equation:
470 = 2(2W + 40) + 2W
Now simplify and solve for W:
470 = 4W + 80 + 2W
470 - 80 = 6W
390 = 6W
W = 390/6
W = 65
Now that you have the value of W, substitute it back into the first equation to find L:
L = 2(65) + 40
L = 130 + 40
L = 170
Therefore, the width of the garden is 65 yards and the length is 170 yards.