To find the perimeter, we have to find AB which is the hypothenuse of the right triangle ADB. Let's use Pythagorean's Theorem.
[tex]AB^2=BD^2+AD^2[/tex]Replacing the given values, we have.
[tex]\begin{gathered} AB^2=4^2+3^2 \\ AB=\sqrt[]{16+9}=\sqrt[]{25} \\ AB=5 \end{gathered}[/tex]Given that AB = BC, then BC = 5.
Moreover, remember that the perimeter is the sum of all sides.
[tex]P=5+5+3+3=16[/tex]