By solving a system of equations, we will see that the parking lot is 210ft by 200ft.
How to get the dimensions of the parking lot?
For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = L*W
Here we know that the perimeter is 820 ft and the area is 42,000 ft²
Then we can write the two equations (ignoring units).
820 = 2*(L + W)
42,000 = L*W
We can isolate L in the first equation to get:
820/2 = L + W
410 - W = L
Now we can replace that in the other equation:
42,000 = (410 - W)*W = 410*W - W^2
Now we want to solve the quadratic equation:
-W^2 + 410*W - 42,000 = 0
The solutions are given by:
[tex]W = \frac{-410 \pm \sqrt{410^2 - 4*(-1)*(-42000)} }{-2} \\\\W = \frac{-410 \pm 10 }{-2}[/tex]
Then the solutions are:
W = (-410 + 10)/(-2) = 200
W = (-410 - 10)/2 = 210
If we take W = 200, then:
L = 410 - W = 410 - 200 = 210
So we can conclude that the parking lot is 200ft by 210ft.
If you want to learn more about rectangles:
https://brainly.com/question/17297081
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