Quadratic Word Problems

Question

The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units. What is the width, in units, of the rectangle?

Answer 1

6 by 3

length=6, width =3

Area = wL = 18

L=18/w

w=L-3

L=w+3

A=Lw= (w+3)w = 3w+w^2=18

w^2+3w -18 =0

(w+6)(w-3)=0

w=3 units wide

L=3+3=6 units long

ignore the w=-6, L=-3 solution unless you're in a universe with negative dimensions or the twilight zone

another way to solve for w and L is just try some integer factors of 18 which are 18, 9, 6, 3, 2 and 1 only 6 and 3 are 3 apart