A Rectangular Parking Lot

Question

A rectangular parking lot has a length that is 9 yards greater than the width. The area of the parking lot is 400 square yards. Find the length and the width.

Answer 1

Let x = width

Let x+9=length

Area = length x width Plug the values and expression into the equation to get:

x(x+9)=400 Distribute

x²+9x=400 Subtract 400 from both sides and simplify

x²+9x-400=400-400

x²+9x-400=0

Now need to solve this. You can solve by factoring. You could also use the quadratic equation

x²+9x-400=0

(x+25)(x-16)=0

Set each factor to 0 and solve

(x+25)=0 Subtract 25 from both sides

x=-25 (Cannot be the answer, width can't be negative)

(x-16)=0 Add 16 to both sides

x=16 is the width

x+9 = 16+9 = 25 is the length

The dimensions of the parking lot are the width is 16 yds and the length is 25 yds.