# Stewart's Theorem

Pronunciation: /ˈstʊ.əɹtz ˈθɪər.əm/ Explain
Stewart's Theorem relates the length of the sides of a triangle to a cevian of the triangle:

`b`^{2}m + c^{2}n = a(d^{2} + mn) where

`a`,

`b`, and

`c` are lengths of sides of the triangle and

`m` and

`n` are the lengths of the segments into which

`a` is divided by the cevian.

### References

- McAdams, David E.. All Math Words Dictionary, stewart's theorem. 2nd Classroom edition 20150108-4799968. pg 171. Life is a Story Problem LLC. January 8, 2015. Buy the book

### Cite this article as:

McAdams, David E. Stewart's Theorem. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/stewartstheorem.html.
### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (

McAdams, David E.)
5/5/2011: Initial version. (

McAdams, David E.)