Arectangular field has dimensions of (2x-3) yards and (x+4) yards. the area of the field is 285 square yards. what are the length and width of the field?

The area of a rectangle is given by the multiplication of its dimensions:

In this case, we have an exact value for the area, and two variable expressions for width and length. Let's replace the formula above with what we're given:

If you expand the right hand side, you have

And if you move all terms to the right hand side, this becomes

This is a quadratic equation, since it is in the form , where

If you plug these values in the generic formula

you get

Let's see which dimensions they yield:

But the dimensions of a rectangle can't be negative, so we can't accept this answer.

The other solution yields

So these are the dimensions of the rectangle