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## Answers

Let us assume that each side of triangle ABC is ‘a’

Then, BD = a/3, MC = a/2 and

DM =2a/3 -a/2 =a/6

also, AM = a√3/2

According to Pythagoras theorem, in triangle ADM;

AD² =AM²+DM²

OR ,AD² =(a√3/2)² +(a/6)²

=3a²/4+a²/36

=27a²+a²/36

AD² =28a²/36 = 7a²/9

=7AD² =9a²

=7AD² =9AB² ......PROVED