- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
$AM$ is a median of a triangle $ABC$.
Is $AB + BC + CA > 2 AM?$ [Consider the sides of triangles $∆ABM$ and $∆AMC$.]"
Given: $AM$ is a median of a triangle $ABC$.
To do: To find whether $AB + BC + CA > 2 AM?$
Solution:
Let us consider $\Delta ABM$ and $\Delta AMC$
It is a known fact that the sum of the triangle of any two sides in a triangle should be greater than the length of the third side.
In $\Delta ABM$:
$AB+BM>AM$ ......$(i)$
In $\Delta AMC$:
$AC+MC>AM$ ......$(ii)$
Let us add $(i)$ and $(ii)$
$AB+BM+AC+MC>AM+AM$
$\Rightarrow AB+AC+(BM+MC)>2AM$
$\Rightarrow AB+AC+BC>2AM$
Hence proved!
Advertisements