Hi Forum!

I found an interesting question.

In triangle ABC, the median from vertex A is perpendicular to the other median from vertex B. If the lengths of sides A and B are 6 and 7 respectively, then the length of AB is?

I managed to do some of it. I got impressed with the solution, since it was somehow complex.

It says, that the ratio of the medians will be 2:1 because they are perpendicular.

Can this be proved? I don't understand the line of thought here.

What median is mentioned? We can have

,

or

.

Calculating

it gets easy to find AB.

So, this involves a little bit of Pythagorean Theorem and Apollonius' Theorem.

But the problem here is the usage.

It is difficult to find a way to solve it without a graph too.

Thanks.