Question

In the diagram below, if the red lines are medians, and segment AE = 21, would be the length of the segment AO?

Answer 1

We have a triangle with its medians AE, FB, and CD. The medians intersect at point O, which is called the centroid of the triangle.

The centroid is always 2/3 of the length of the median from each vertex.

Therefore if AE = 21, then AO must be 2/3 of that.

`\begin{gathered} AO=(2)/(3)AE \\ \\ AO=(2)/(3)(21) \\ \\ AO=14 \end{gathered}`

The answer is option A, 14.