A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 520 feet of fencing to fence off the other three sides.
width
length
It could be 150 by 185.
Of course many other dimensions are possible.
Let's solve this step-by-step:
1. Let's assume the width of the parking lot is "w" feet.
2. Since the parking lot is rectangular, the opposite side will also have the same width, so the total width will be 2w.
3. We know that the length of the parking lot can be calculated by subtracting the width from the total fencing length: length = 520 - 2w.
4. The perimeter of the parking lot is the sum of all sides. In this case, it will be the width, length, and twice the width, which is 2w.
Perimeter = width + length + 2w = w + (520 - 2w) + 2w = 520 + w.
5. According to the problem, the perimeter of the parking lot is equal to the given fencing length of 520 feet. So we can set up the equation: 520 + w = 520.
6. Subtracting 520 from both sides of the equation, we get: w = 520 - 520 = 0.
7. Since the width cannot be zero in this context, there must be an error in the problem statement. Please double-check the given information.
I hope this helps! Let me know if you have any further questions.
To find the dimensions of the rectangular parking lot, we can use the information given in the problem. Let's assume the width of the parking lot is w feet, and the length is l feet.
We know that the total amount of fencing used is 520 feet. Since three sides of the parking lot will be fenced (excluding the side bordered by the highway), we can set up the equation:
2w + l = 520
Now, let's simplify this equation. Since we need to isolate either w or l, let's solve for l in terms of w:
l = 520 - 2w
Now we have an expression for the length in terms of the width.
To find the dimensions that will maximize the area of the parking lot, we need to consider the fact that the area of a rectangle is given by the formula:
Area = length * width
Let's substitute the expression for the length (520 - 2w) into the area formula:
Area = (520 - 2w) * w
Now, we can expand this equation:
Area = 520w - 2w^2
To find the maximum area, we need to find the value of w that maximizes this equation. This can be done by finding the vertex of the quadratic equation. The x-coordinate of the vertex can be found using the formula:
x = -b / (2a)
In our case, a = -2, and b = 520. Substituting these values, we get:
w = -520 / (2 * -2) = 130
Now that we have the value for w, we can substitute it back into the equation for the length to find the value of l:
l = 520 - 2w = 520 - 2 * 130 = 520 - 260 = 260
Therefore, the width of the parking lot is 130 feet, and the length is 260 feet.