Answer:
the correct answer is B) 205 ft.
Explanation:
Let's start by using the information given to set up a system of equations to solve for the dimensions of the rectangular parking lot.
Let's call the length of the parking lot L and the width W. We know that the perimeter of the parking lot is 820 feet, so we can write:
2L + 2W = 820
We also know that the area of the parking lot is 42,000 square feet, so we can write:
L * W = 42,000
We now have two equations and two unknowns. We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for W:
2L + 2W = 820
2W = 820 - 2L
W = (820 - 2L) / 2
We can now substitute this expression for W into the equation for the area of the parking lot:
L * W = 42,000
L * [(820 - 2L) / 2] = 42,000
Multiplying both sides by 2 to eliminate the denominator:
L * (820 - 2L) = 84,000
Expanding and rearranging:
-2L^2 + 820L = 84,000
2L^2 - 820L + 84,000 = 0
We can now solve this quadratic equation for L using the quadratic formula:
L = [820 ± sqrt(820^2 - 4 * 2 * 84,000)] / (2 * 2)
L = [820 ± sqrt(672,400)] / 4
L = [820 ± 820] / 4 or L = [820 ± 180] / 4
L = 250 or L = 145
If L = 250, then W = (820 - 2L) / 2 = 160. However, this does not satisfy the equation for the area of the parking lot (L * W = 42,000).
If L = 145, then W = (820 - 2L) / 2 = 215. This satisfies both equations, so the dimensions of the parking lot are L = 145 feet and W = 215 feet.
Therefore, the correct answer is B) 205 ft.