Firstly, we need to draw triangle
we know that
O is a centroid
and centroid divides median into 2:1
so,
[tex]\frac{CO}{FO} =\frac{2}{1}[/tex]
we have FO=4
so, we can plug it
[tex]\frac{CO}{4} =\frac{2}{1}[/tex]
[tex]CO=8[/tex]
now, we can find CF
CF=OC+FO
CF=8+4
CF=12
now, we can see triangle ACF is a right angled triangle
so, we can use pythagoras theorem
[tex]x^2=(\frac{x}{2} )^2+12^2[/tex]
now, we can solve for x
[tex]\frac{3x^2}{4}=144[/tex]
[tex]x^2=192[/tex]
[tex]x=8\sqrt{3}[/tex]
Since, it is equilateral triangle
so,
[tex]AC=x=8\sqrt{3}[/tex]
we know that
E is a mid-point
so,
[tex]AE=\frac{AC}{2}[/tex]
now, we can plug values
[tex]AE=\frac{8\sqrt{3}}{2}[/tex]
[tex]AE=4\sqrt{3}[/tex]................Answer
Answer:
Your answer choice would be C) 8.
Step-by-step explanation:
