Answer:
12, D
Step-by-step explanation:
There are a few general rules for special triangles, the 45-45-90 triangle among them.
If the value of one of the two sides that isn't the hypotenuse is x, the value of the hypotenuse is x times the square root of 2.
So basically, if x = 1, then the hypotenuse would be the square root of 2.
(We can use the Pythagorean Theorem to prove this. a^2 + b^2 = c^2, so if a and b are equal to 1, we square them - still leaving us with 1 - then add them to get 2, which is equal to c^2, meaning to get to c we have to take the square root of 2.)
In your case, the value of one of the sides is 6 times the square root of 2. All you have to do is multiply that value by the square root of 2 to get the value of x in your problem!
6 * sqrt(2) * sqrt(2) = 6 * 2 = 12. Which would be answer D in your selection.
