Question

Plz help me ASAP thx.

Answer 1

Use the Pythagorean theorem:

$a^2+(2\sqrt3)^2=(4\sqrt3)^2\\\\a^2+2^2(\sqrt3)^2=4^2(\sqrt3)^2\\\\a^2+4\cdot3=16\cdot3\\\\a^2+12=48\ \ \ \ |-12\\\\a^2=36\to a=\sqrt{36}\\\\\boxed{a=6\to C.}$

Used:

$(a\cdot b)^n=a^n\cdot b^n\\\\(\sqrt{a})^2=a$