Question

I have no idea how to do this. I need some help. Thanks in advance.

Answer 1

if we run a line from a corner(vertex) in a triangle, towards the middle-point of the opposite side, the line we get is called a median, so in this triangle we have three medians, AE, CD and BF.

now, since the median hits the opposite side in the middle, that means two equal halves from that middle

the line where all medians meet inside the triangle is the centroid.  The centroid cuts all medians in a 2:1 ratio, so one side of the median is twice as long as the other side.

we know CD = 18, let's split it in a 2:1 ratio

$\bf 18\qquad 2:1\qquad \cfrac{2}{1}\qquad \cfrac{2\cdot \frac{18}{2+1}}{1\cdot \frac{18}{2+1}}\implies \cfrac{2\cdot 6}{1\cdot 6}\implies \cfrac{12}{6} \\\\\\ \cfrac{GC}{DG}=\cfrac{12}{6}\implies DG=6\qquad GC=12$

we also know that AG = 10, and that AG : GE is a ratio of 2:1, so is AG is 10, then GE must be half that, because AG is twice as much as GE, so GE = 5, and AG + GE = AE, so AE = 15.