Find x in DEF

A. 6
B. 6 (square root 2)
C. 6 (square root 3)
D. 12

B. 6√2

Step-by-step explanation:

We can use the Pythagorean Theorem to solve this out. The Pythagorean Theorem states that for any right triangle with the shortest sides (called legs) as a and b and the longest side (called the hypotenuse) as c:

a² + b² = c²

Here, a = b = 6, so:

6² + 6² = c²

36 + 36 = c²

72 = c²

c = √72 = 6√2

Now, we see the answer is B.

However, there's a trick to solving these kinds of problems. Notice that DEF is both an isosceles triangle and a right triangle. We call these 45-45-90 triangles because those are the angles of the triangle.

One characteristic of these types of triangles is that their leg to leg to hypotenuse ratio is 1 : 1 : √2, always. We could apply that here. We see that the legs are 6, so we could find the hypotenuse simply by multiplying 6 by √2, and we would get 6√2, which is exactly the value we obtained above.

Thus, the answer is B.