Answer:
B. 36+12sqrt(2)
Step-by-step explanation:
We can use Pitagoras' theorem to find the height of the triangle
15^2=9^2 + h^2
h^2=144
Lets apply square root to the whole equation:
sqrt(h^2=144)
h=12
With the height, we can now find the length of AC.
Sin(45)=12/AC.
AC=12/Sin(45)=24/sqrt(2)=12*sqrt(2) if we rationalize.
Now, lets fin the missing segment between B and C (call it)
where 9+x= BC
Cos(45)=x/AC
x=cos(45)*AC=12
Now, the perimeter is the sum of all its sides
AB+AC+BC=15+12*sqrt(2)+9+12=36+12sqrt(2)
