Question

In equilateral ΔABC, AD, BE, and CF are medians. If FO = 4, then AE = A) 4 B) 4 3 C) 8 D) 12

Answer 1

Answer:

Your answer choice would be C) 8.

Step-by-step explanation:

Answer 2

Firstly, we need to draw triangle

we know that

O is a centroid

and centroid divides median into 2:1

so,

$\frac{CO}{FO} =\frac{2}{1}$

we have FO=4

so, we can plug it

$\frac{CO}{4} =\frac{2}{1}$

$CO=8$

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

$x^2=(\frac{x}{2} )^2+12^2$

now, we can solve for x

$\frac{3x^2}{4}=144$

$x^2=192$

$x=8\sqrt{3}$

Since, it is equilateral triangle

so,

$AC=x=8\sqrt{3}$

we know that

E is a mid-point

so,

$AE=\frac{AC}{2}$

now, we can plug values

$AE=\frac{8\sqrt{3}}{2}$

$AE=4\sqrt{3}$................Answer