Question

Find the value of the variables. If your answer is an integer, leave it in simplest radical form.

Answer 1

Method 1

It's the triangle 30 - 60 - 90. The lengths of a side are in proportion 1 : √3 : 2.

6 : 6√3 : 12

Answer: 6√3

Method 2:

Use the Pyhagorean theorem:

$x^2+6^2=12^2\\\\x^2+36=144\ \ \ \ |-36\\\\x^2=108\to x=\sqrt{108}\\\\x=\sqrt{36\cdot3}\\\\x=\sqrt{36}\cdot\sqrt3\\\\\boxed{x=6\sqrt3}$