Math CentralQuandaries & Queries


Question from leeja, a teacher:

In a triangle ABC the sides BC and AC are given. It is also known that the medians to these sides are perpendicular to each other. Calculate the length of AB in terms of the other two given sides.


Stewart's Theorem applied to a median of a triangle is what you will want to use here: If m is the median to the side whose length is a, while b and c are the lengths of the sides attached to one end of the median, then

4m2 = 2b2 + 2c2 - a2.

You will also need Pythagoras and the fact that the medians of a triangle intersect 2/3 of the way from a vertex to the midpoint of the opposite side.


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