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
Kinda stuck here.
2W+2(2W+40) = 470
2W + 4W + 80 = 470
6W = 390
W= 65
Then L = 2(65) + 40 = 170
Your equation made no sense.
How did you plan to work in the 470 ?
Where did it say that the perimeter was 80, which is what your equation claimed.
To solve for the length and width of the garden, we can use the information given and set up a system of equations.
Let's denote the width of the garden as W and the length as L.
We are given that the length of the garden is 40 yards longer than double the width. So, we can write the equation:
L = 2W + 40 ........(Equation 1)
We also know that the perimeter of the garden is 470 yards. The formula for the perimeter of a rectangle is given by:
Perimeter = 2*(Length + Width)
Substituting the values, we have:
470 = 2*(L + W) ........(Equation 2)
Now, let's solve these equations:
Substitute Equation 1 into Equation 2:
470 = 2*((2W + 40) + W)
470 = 2*(3W + 40)
470 = 6W + 80
6W = 470 - 80
6W = 390
W = 390/6
W = 65
Now, substitute this value of W back into Equation 1 to find the length:
L = 2W + 40
L = 2(65) + 40
L = 130 + 40
L = 170
Therefore, the length of the garden is 170 yards and the width is 65 yards.
To solve the problem, you need to solve the equation that describes the relationship between the length and the width of the garden.
Let's analyze the information given:
1. The length of the garden is 40 yards longer than double the width.
This can be expressed as L = 2W + 40.
2. The perimeter of the garden is 470 yards.
The formula for the perimeter of a rectangle is P = 2L + 2W.
Now, substitute the expression for L (from equation 1) into the perimeter equation (equation 2):
470 = 2(2W + 40) + 2W
To solve for W, distribute the 2 to the terms inside the parentheses:
470 = 4W + 80 + 2W
Combine the like terms:
470 = 6W + 80
Next, isolate W by subtracting 80 from both sides:
470 - 80 = 6W
390 = 6W
Finally, divide both sides by 6 to find the value of W:
W = 65
Now, plug this value of W back into equation 1 to find L:
L = 2W + 40
L = 2(65) + 40
L = 130 + 40
L = 170
Therefore, the width of the garden is 65 yards, and the length is 170 yards.