SOLUTION: a rectangle parking lot has a length that is 3 yards greater than the width. The area of the rectangular lot is 180 square yards. find the length and the width.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a rectangle parking lot has a length that is 3 yards greater than the width. The area of the rectangular lot is 180 square yards. find the length and the width.      Log On


   

Question 73356: a rectangle parking lot has a length that is 3 yards greater than the width. The area of the rectangular lot is 180 square yards. find the length and the width.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=width of parking lot
Then x+3=length of parking lot
Area of rectangle equals Length times Width. So our equation to solve is:
180=x%28x%2B3%29 get rid of parens
180=x%5E2%2B3x subtract 180 from both sides
x%5E2%2B3x-180=0 quadratic in standard form
A=1
B=3
C=-180
We will solve using the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-3+%2B-+sqrt%28+3%5E2%2B4%2A180+%29%29%2F%282%29+
x+=+%28-3+%2B-+sqrt%28+9%2B720+%29%29%2F%282%29+
x+=+%28-3+%2B-+sqrt%28+729%29%29%2F%282%29
x+=+%28-3+%2B-+27%29%2F%282%29
x=-30%2F2=-15-------------------------discount the negative value for length
x=%2B24%2F2=12+yds -------------------------width of field
x%2B3=12%2B3=15+yds---------------------------length of field
CK
15*12=180
180=180
also 15 is 3 more than 12
Hope this helps---ptaylor