Question

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?
120 ft
205 ft
210 ft
375 ft

Answer 1

Let the sides be x and y. Then x + y = 410 and xy = 42,000. Substitute y = 410 − x:

x(410 − x) = 42,000 → x^2 − 410x + 42,000 = 0.

Discriminant = 410^2 − 4·42,000 = 100, so x = (410 ± 10)/2 = 210 or 200.

Thus one dimension is 210 ft (the other is 200 ft). Answer: 210 ft.