Arectangle has an area of 40 square units. the length is 6 units greater than the width.
what are the dimensions of the rectangle?

Let be the width.  We write a quadratic equation, using the fact that area = length times width:



There are two easy ways to solve this from here.  First, we can simply guess and check.  To do this, simply guess a value for and find for that value.  Then, guess a higher value of if your result is too small, or a lower one if it is too big.  Doing this should give you relatively quickly.

Alternatively, we can solve it as a quadratic.  Expanding and moving terms to one side gives:



The easiest way to solve this quadratic is to factor it:



One of the two terms on the LHS must be zero, so .   since the width must be greater than zero, so .  Thus, the width is and the length is .