Question

What is the perimeter of ABC?

Answer 1

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)