Question

AD is perpendicular to the side BC of an
equilateral triangle ABC. Prove that 4AD2 = 3AB2.​

Answer 1

Answer:

given- ABC is an equilateral triangle

to prove that - 3AB2=4AD2

proof - by pythagoras theorem in triangle ABD

AB2 = AD2 + BD2

but BD = 1/2 BC

thus AB2 = AD2 + {1/2 BC}2

AB2 = AD2 + 1/4 BC2

4 AB2 = 4AD2 + BC2

4 AB2 - BC2 = 4 AD2

thus 3AB2=4AD2 { as AB =BC we can subtract them}