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.