Question

A rectangular parking lot with a perimeter of 440 feet is to have an area of at least 9000 square feet. within what bounds must the length of the rectangle lie (in feet)?

Answer 1

l + w = 220

lw ≥ 9,000

l(220 - l) ≥ 9,000

220l - l² ≥ 9,000

l² - 220l + 9,000 ≤ 0

l = (220 ± √(220² - 4(9,000)))/2

= (220 ± √12,400)/2

= (220 ± 20√31)/2

= 110 ± 10√31

110 - 10√31 < l < 110 + 10√31

54.32 < l < 165.68