Suppose you have 36 yards of fencing to build a fence around a rectangular backyard garden. The width is 18 yards less than twice the length. Find the length and width of this garden.
l = length
w = width = 2l - 18
P = 2l + 2w
36 = 2l + 2(2l - 18)
Can you solve from here?
To find the length and width of the garden, we can set up a system of equations using the given information.
Let's denote the length as "L" and the width as "W".
From the given information, we know that the perimeter of the garden is 36 yards, which means that the sum of all sides is 36 yards:
Perimeter = 2L + 2W = 36
We also know that the width is 18 yards less than twice the length:
W = 2L - 18
Now, we can solve the system of equations to find the values of L and W.
Step 1: Substitute the value of W from the second equation into the first equation:
2L + 2(2L - 18) = 36
Simplify:
2L + 4L - 36 = 36
Combine like terms:
6L - 36 = 36
Step 2: Add 36 to both sides of the equation to isolate the variable term:
6L = 36 + 36
Simplify:
6L = 72
Step 3: Divide both sides of the equation by 6 to solve for L:
L = 72 / 6
Simplify:
L = 12
Now that we have the value of L, we can find the value of W by substituting L back into the second equation:
W = 2(12) - 18
Simplify:
W = 24 - 18
W = 6
Therefore, the length of the garden is 12 yards and the width is 6 yards.