If James draws a diagonal line of length x from one right angle to the opposite right angle, then he divides his piece of paper into two pieces, each of them is right triangle with legs 9 inches and 12 inches.
By Pythagorean theorem:
[tex]x^2=9^2+12^2 \\ x^2=81+144 \\ x^2=225 \\ x=15[/tex] inches.
Answer: 15 inches