Question 1740
(Please ignore all dotted lines [---] in the pictures.  They are there so the picture would come out right.)

Suppose your original square has side length x:
   _____
  |-------|
  |-------| x
  |_____|
     x         (not to scale)

Then its area is {{{ x^2 }}}.  Doubling the base gives the following shape:

   __________
  |-------------|
  |-------------| x
  |__________|
       2x              (not to scale)


Shrinking the height by 3 inches gives the following shape:


   __________
  |-------------| x-3
  |__________|
       2x              (not to scale)


The area of this new rectangle is {{{ 2*x*(x-3) = 2x^2 - 6x }}}.

This area is 40 square inches larger than the area of the original square.  

Recall that the area of the original square is {{{ x^2 }}}.  
This gives us the equation {{{ x^2 + 40 = 2x^2 - 6x }}}.  

Subtracting {{{ x^2 }}} from both sides gives {{{ 40 = x^2 - 6x }}}.  

Then we subtract 40 from both sides to get {{{ 0 = x^2 - 6x - 40 }}}.  

We can factor this into {{{ 0 = (x-10)*(x+4) }}}, which means x = 10 or 
x = -4.  

Since x represents the length of the side of a square, x cannot be less than zero.  Hence, x = 10 inches.