Q. 113.7( 6 Votes )

ΔABC is an equila

Answer :

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Δ ABC is an equilateral triangle.


Also, BC = AB = AC = 2a


The AD, CE, and BF are the altitude at BC, AB and AC respectively. Therefore, D, E, and F are the midpoint of BC, AB and AC respectively.


Now, ΔADB and ΔADC are right-angled triangles.


Applying Pythagoras theorem,


AB2 = BD2 + AD2


(2a) 2 = a2 + AD2


AD2 = 3a2


AD = a√3 units


Similarly ΔACE and ΔBEC are right-angled triangles.


Applying Pythagoras theorem,


CE = a√3 units


And ΔABF and ΔBFC are right-angled triangles.


Applying Pythagoras theorem,


BF = a√3 units


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