Final answer:
To find the length of a rectangular lot with a perimeter of 132 feet, we need to set up a system of equations based on the given information. The length of the lot is three more than twice the width. By substituting the values and solving the equations, we find that the length is 45 feet.
Step-by-step explanation:
To find the length of a rectangular lot with a perimeter of 132 feet, we need to set up a system of equations based on the given information. Let's denote the width of the lot as 'w' and the length as 'l'. The perimeter of a rectangle is calculated by adding twice the width to twice the length, so we can write the equation:
P = 2w + 2l
In this case, the perimeter is given as 132 feet, so we have:
132 = 2w + 2l
The question also tells us that the length is three more than twice the width, so we can write another equation:
l = 2w + 3
Now we can substitute this expression for 'l' in the first equation:
132 = 2w + 2(2w + 3)
Simplifying this equation, we get:
132 = 2w + 4w + 6
Combining like terms, we have:
132 = 6w + 6
Subtracting 6 from both sides:
126 = 6w
Dividing both sides by 6, we find:
w = 21
Now we can substitute this value back into the expression for 'l' to find the length:
l = 2(21) + 3
Simplifying, we get:
l = 42 + 3
l = 45
Therefore, the length of the rectangular lot is 45 feet.