How can I create a unique word problem that needs to be solved using a quadratic equation?

There was a nice geometry problem i saw yesterday...

A rectangle's length is 3 times its width.  If both its length and width are increased by 2, the area is 32 cm.  What is the original length of the rectangle?

This ends up being a quadratic problem which requires you to solve, and eliminate one root as the length can't be negative.  I thought it was very nice.

why dont you try to do the vertical distance covered bny a ball which is thrown at a certain speed as a functon of time
s = ut -1/2gt^2 you will notice for every s that you take there will be two times, which shows it occupies the same height at two different times , how ? its obvious because when you throw it up it reaches a certain height and when it is falling down it crosses the same height
this is a good examplke of using quadratics
you can test the same way projectile motion but im not sure which grade you are in
all the best