Answer:
\(2\sqrt{18}+6 \ in\)
Step-by-step explanation:
As ABC is an isosceles triangle, the segment CD cuts to AB in two equal parts. Then, AD=DB=3 in. Now, using Pitagoras Theorem we have that:
\(CD^2+DB^2 = BC^2\)
\(3^2+3^2 = BC^2\)
\(BC = \sqrt{3^2+3^2}\)
\(BC = \sqrt{9+9}\)
\(BC = \sqrt{9+9}\)
\(BC = \sqrt{18}=AC\).
Now, the perimeter is the sum of the three sides of the triangle, then
\(perimeter = AC+BC+AB = \sqrt{18}+\sqrt{18}+6 = 2\sqrt{18}+6 \ in\).
