Question

In an equilateral triangle abc ad perpendicular to bc prove 3bc2 = 4ad2

Answer 1

REFER TO THE ATTACHMENT...

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Answer 2

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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

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