Question 1204973
<br>
Here is an easy way to find the answer.<br>
The perimeter is 520 feet, and the area has to be at least 12000 square feet.<br>
The maximum area with a given perimeter is if the rectangle is a square; the side length of the square would be 130 feet.  So<br>
Let 130+x be the length of the parking lot
then 130-x is the width of the parking lot<br>
The area is greater than or equal to 12000:<br>
{{{(130+x)(130-x)>=12000}}}
{{{16900-x^2>=12000}}}
{{{x^2<=4900}}}
{{{x<=70}}}<br>
To have an area of 12000 square feet or more, the length can be 130+x, where the maximum value of x is 70 (and, or course, the minimum value is 0).  That means the length can be anywhere from 130 feet to 130+70 = 200 feet.<br>
ANSWER: The possible lengths are from 130 to 200 feet<br>