Nathaniel B. answered • 10/03/17

Economist, Math Lover, and Veteran with diverse teaching experience

We know that L=2w+3 from the problem and since Area is 54 square ft, then L*w=54, therefore...

54=(2w+3)*(w)

54=2w^2+3w

2w^2+3w-54=0

Now you have your quadratic equation!

Since you know it has rational roots, you can attempt to solve by factoring.

(w+6)(2w-9)=0. Next you separate the factors,

w+6=0 2w-9=0

w=-6 w=(9/2)

Since we are looking for the lengths of a rectangle, our answer cannot be negative, so we through away (w=-6) and just keep w=(9/2)

So to find length, let's plug it back into the original L equation

L=2w+3

L=2(9/2)+3

L=9+3

L=12

Hope this helps! Let me know if you have any more questions or any follow-up that I can help you with!

Nathaniel