What is the length of x in the diagram below? A triangle with vertical bisector forms 2 triangles with a right angle. One triangle has a side length of 5 and another angle with a measure 45 degrees. Another triangle has a hypotenuse with length x and another angle with measure 30 degrees.
StartFraction 5 Over StartRoot 3 EndRoot
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
5 StartRoot 3 EndRoot
10

That is a 45-45-90 triangle next to a 30-60-90 triangle.  

So, the height of the left triangle equals 5.

That makes the short side of the 30-60-90 triangle also equal to 5.

In a 30-60-90 triangle, the hypotenuse (or "x") is exactly twice the length of the shortest side.

Therefore, the hypotenuse (or "x") equals 10.

Step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11