Answer :



Given, ABC is a equilateral triangle where AB = BC = AC and BD = BC


Draw AE perpendicular BC


Δ ABE Δ ACE


BE = EC =


Now in Δ ABE, AB2 = BE2 + AE2


also AD2 = AE2 + DE2


AB2 –AD2 = BE2 – DE2


= BE2 – (BE-BD)2


= ()2


= ()2


AB2-AD2 = 2


Or 7 AB2 = 9 AD2


Hence, proved


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