Question

medal and fan **
what is the value of the variable in the given figure in simplest radical form? A.x=12sqrt3 B. x=6sqrt3 C.x=6 D.x=3

Answer 1

It's a right triangle. So use the Pythagorean theorem to solve.

\[x ^{2} + 6^{2}=12^{2}\] \[x ^{2} = 12^{2}- 6^{2}\]\[x=\sqrt{144-36}\]\[x=\sqrt{108}\]\[x=\sqrt{36*3}\]\[x=\sqrt{36}*\sqrt{3}\]\[x=6\sqrt{3}\]

Or if you had memorized the sides of a 30-60-90 right triangle, then you would've knew that the shorter leg is x. The hypotenuse is 2x, and the longer leg is\[x \sqrt{3}\]and you would have gone directly to \[6\sqrt{3}\]