AutoCad :: Rectangle - Find Out Longest One

I have a rectangle that is 100 x 144 inches. I need to find out the longest rectangle that I can make from it.

So far, the longest and widest (widest?) that I've found is 147.75 x 30.9 inches. I must hold the 147.75 but I need it to be wider than 30.9 inches. What's the best way to do this?

Here's how I've been doing it:

I draw the block (100 x 144)
I make a circle with a radius of 147.75
I move the center of the circle in various places on the block and find the tangents of circle to block
I then make right angles and see what I've got

There must be a better way to do this.