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These are special triangles. The triangle with a hypotenuse of 11 is a 30-60-90 triangle, and the other triangle in the diagram is a 45-45-90 triangle. For such triangles, the following properties apply.

For 30-60-90 triangles:

If the short leg is x -

· the hypotenuse is 2x

· the long leg is x√(3)

For 45-45-90 triangles:

Their legs are congruent. If their legs are x -

· the hypotenuse is x√(2)

We can find x by determining the length of the legs of the 45-45-90 triangle and using the above property. Notice that one of the legs of the 45-45-90 triangle is also the long leg of the 30-60-90 triangle. By finding the length of the long leg of the 30-60-90 we can determine the length of the hypotenuse of the 45-45-90 triangle.

The hypotenuse measures 11. The long leg is √(3) times the length of the short leg. The short leg is half the hypotenuse, thus the short leg is 5.5. The long leg is 5.5√(3) or . Since this is the length of the legs of the 45-45-90 triangle, the hypotenuse (x) is .

Simplify.

D.