A college is creating a new rectangular parking lot The leng

A college is creating a new rectangular parking lot. The length is 0.14 mile longer than the width and the area of the parking lot is 0.048 square mile. Find the length and width of the parking lot.

The width of the parking lot is ____ mile. (Type an integer or a decimal.)

The length of the parking lot is    _____mile.

Solution

Let the width of the rectangular park be x miles.

The length of the rectangular park is = (x+0.14) miles.

The area of the rectangular park is = 0.048 square mile.

Therefore,

x*(x+0.14) = 0.048

x^2+0.14x-0.048 = 0, multiply this equation with 1000 gives

1000x^2+140x-48 = 0

250x^2+35x-12=0, use quadratic formula to get

x = (-35+sqrt(1225+12000))/500, (-35-sqrt(1225+12000))/500

x = (-35 + 115)/500 = 0.16, (-35 - 115)/500

But x must be a positive number. Hence ignore negative value of x.

x = 0.16 miles.

The width of the rectangular park is 0.16 miles.

The length of the parking lot is = 0.16 + 0.14 = 0.3 miles.