We need to find the length of AC.
We can tell that one right triangle has sides of 6, 8, and 10.
The other right triangle has two legs with sides of 8. The hypotenuse of this triangle is the length of AC.
\(AC = \sqrt{8^2 +8^2} = \sqrt{64+64}=\sqrt{128} =\sqrt{2\cdot64} = 8\sqrt{2}\)
Now we can find the perimeter:
\(10 + 6 + 8 + 8\sqrt{2} = \boxed{\bf{24 + 8\sqrt{2}}\approx35.314}\)
