Question

In an equilateral triangle ABC,if AD⟂ BC,then prove that 3AB²=4AD²
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

Step-by-step explanation:

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}