Question

in an equilateral triangle ABC, AD perpendicular BC . Prove that
$3a {b}^{2} = 4a {d}^{2}$
​

Answer 1

Answer: proved

Step-by-step explanation:

Let side of he triangle be "a"

let height of the triangle be "h"

so in triangle ABD

by Pythagoras theorem

a sq = h sq = a/2 sq   (since bd = a/2)

a sq - a sq / 4 = h sq

4a sq - a sq / 4 = h sq

3a sq = 4h sq

a= BC , h=AD

SO

3BC sq = 4 ADsq

hence proved