Quandaries
and Queries 

This is a 9th grade geometry problem: In triangle ABC, AB=4, AC=6 and AD=5, where D is the midpoint of BC. Determine BC. 

Hi Amy, There is a formula known as Stewart's theorem that deals with a more general problem. Let's use the standard notation: a = BC, b = AC, c = AB, and let m = AD = our median from A. Then Stewart's theorem tells us that
This formula comes from applying the cosine law to the triangle ABD, then replacing cos B by (a^{2} + c^{2}  b^{2})/2ac. [For the record, Stewart's theorem tells us that if the point D divids BC into segments of length r = BD and s = DC, and AD has length p, then
Here in your problem, r = s = a/2.] Chris


