Answer
$AB=3\sqrt{7}$.
Work Step by Step
The given values are
$AC=12$ and $BC=9$
Use the Pythagorean theorem.
$\Rightarrow AB^2+BC^2=AC^2$
Substitute all values
$\Rightarrow AB^2+(9)^2=(12)^2$
Clear the parentheses.
$\Rightarrow AB^2+81=144$
Subtract $81$ from both sides.
$\Rightarrow AB^2+81-81=144-81$
Simplify.
$\Rightarrow AB^2=63$
Take square root both sides.
$\Rightarrow AB=3\sqrt{7}$.
