To answer this we apply the Pythagorean Theorem, this states that given a right triangle with a hypotenuse -longest side- ([tex]a[/tex]) and two sides ([tex]b[/tex] and [tex]c[/tex]), then:
[tex]a^2=b^2+c^2[/tex]
So, for your problem, we can see right triangle with a hypotenuse of 8 ([tex]a=8[/tex]), one side equal to 4 ([tex]b=4[/tex]) and other side unknown; this means we have the following:
[tex]8^2=4^2+x^2[/tex]
We can easily solve for [tex]x[/tex] (altitude of the equilateral triangle):
[tex]x= \sqrt{8^2-4^2}= \sqrt{64-16}= \sqrt{48}=4 \sqrt{3} [/tex]
Hence, the answer is E.
