I'm studying for a test and i seriously can't figure this out. i took a screenshot. and . : ) : p : d

Hello there!

What we are dealing with is called "Pythagorean Theorum", also known as the famous equation "A^2 + B^2 = C^2." The side length "A" is usually the side length opposite of the hypotenuse, which is the side length "C" that is directly across from the right angle of the triangle. The side length "B" is adjacent to the hypotenuse.

Let's apply this to our current triangle.

We have the side length "A", which is 12 in., and our side length "B", which is 6 in.

Now, let's plug in our numbers to our variables in order to solve for C.

A^2 + B^2 = C^2
Replace A with 12 and B with 6.

12^2 + 6^2 = C^2
Simplify the exponents.

144 + 36 = C^2
Simplify the left side.
180 = C^2.

Now, we must solve for C. As C is being squared, we must apply the opposite mathematical term, which is square rooting.

C^2 = 180.
Square root both sides to solve for C.

C =  in.

Your answer is (C).

I hope this helps!

The decimal expansion would be .27 repeated