A rectangular parking has a perimeter of 28 units. The length is six less than double the width. What is the length of the parking lot?
l=2w-6
2l+2w=28
2(2w-6)+2w=28
4w-12+2w=28
w=6.67
l=7.33
To find the length of the parking lot, we need to set up an equation based on the given information.
Let's assume the width of the parking lot as 'w' units.
According to the problem, the length of the parking lot is six less than double the width, which can be expressed as 2w - 6.
The formula for the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
Given that the perimeter is 28 units, we can substitute the values into the formula and solve for the length.
28 = 2(2w - 6 + w)
First, let's simplify the equation:
28 = 2(3w - 6)
Now distribute the 2:
28 = 6w - 12
Next, isolate the variable by moving -12 to the other side of the equation:
28 + 12 = 6w
40 = 6w
Finally, divide both sides by 6 to solve for w:
w = 40/6
w = 20/3
Therefore, the width of the parking lot is 20/3 units.
To find the length, substitute the width value back into one of the expressions we previously determined:
l = 2w - 6
l = 2(20/3) - 6
l = 40/3 - 18/3
l = 22/3
Hence, the length of the parking lot is 22/3 units.