Answer:
x = +√96 = +√(16*6) = + 4√6
Step-by-step explanation:
Note that this is a large triangle with 2 smaller, similar triangles inside. The base of the large triangle is 10, so the base of either of the smaller triangles is half that, or 5. These are all right triangles. We can now apply the Pythagorean Theorem to find x.
According to this Theorem, x² + 5² = 11², so that x² = 121 - 25 = 96.
Taking the positive square root to be the desired side length x,
x = +√96 = +√(16*6) = + 4√6
