In an equilateral triangle abc ad perpendicular to bc prove 3bc2 = 4ad2
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in triangle ABC,
sides are 'a' units
as AD is perpendicular to BC ,
then in triangle ABD ,
AB2 = AD2 + BD2
a2 = AD2 + (a/2)2 [ since AD is perpendicular to BC ]
a2 - a2/4 =AD2
= 3a2 /4 = AD2 ..........(1)
in triangle ADC,
AC2 = AD2 + CD2
a2 = AD2 + (a/4)2
3a2/4 = AD2 .........(2)
from equation 1 and 2
3 a2 /4 = AD2
3 a2 = 4 AD2
3 AB2 = 4AD2 [since AB = a ]
hence proved
HOPE THIS WOULD HELP YOU OUT
in triangle ABC,
sides are 'a' units
as AD is perpendicular to BC ,
then in triangle ABD ,
AB2 = AD2 + BD2
a2 = AD2 + (a/2)2 [ since AD is perpendicular to BC ]
a2 - a2/4 =AD2
= 3a2 /4 = AD2 ..........(1)
in triangle ADC,
AC2 = AD2 + CD2
a2 = AD2 + (a/4)2
3a2/4 = AD2 .........(2)
from equation 1 and 2
3 a2 /4 = AD2
3 a2 = 4 AD2
3 AB2 = 4AD2 [since AB = a ]
hence proved
HOPE THIS WOULD HELP YOU OUT
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