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if AD perpendicular to BC then d is themid point of BC;BD=DC=BC/2=A/2 units
triangle ADC is a right angled triangle.
Then by Pythagoras theorem,
AD square=AC square- DC square=a square-(a) square/4
4a square-a square/4=3a square/4 =AD =√3 a square/4=√3/2 a units
hence√3/2 a proved
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