The pythagorean theorem states that the hypotenuse of a right triangle is the square root of the sum of the squares of the legs: if [tex]h[/tex] is the hypotenuse and [tex]l_1,l_2[/tex] are the legs, we have
[tex]h^2=l_1^2+l_2^2[/tex]
In your case, the legs are 9 and 12, so the hypotenuse is
[tex]h^2 = 9^2+12^2=81+144=225[/tex]
and thus
[tex]h=\sqrt{225}=15[/tex]
