A parking lot for a new ice cream stand has an area of 5000 square yards. The length of the lot is 50 yards longer than its width. Determine algebraically the dimensions of the parking lot, in yards.

length = 50 + 50 = 100 yards

width = 50 yards

Step-by-step explanation:

The area of parking lot for the the ice cream stand is given as 5000 yard². The length of the yard is 50 yard longer than its width.

Let

width = a

length = 50 + a

The parking lot is definitely a rectangle.

Area of a rectangle = length * width

area = (50 + a) a

5000 = (50 + a) a

5000 = 50a + a²

a² + 50a - 5000 = 0

The numbers that can be multiply together to give you - 5000 is - 50 and 100 and this same number can be added to give 50. Therefore,

a² - 50a + 100a - 5000 = 0

a (a - 50) + 100 (a - 50) = 0

(a + 100) (a - 50) = 0

a = - 100 or 50

We can't use negative value so we use 50.

length = 50 + 50 = 100 yards

width = 50 yards