Question

In an equilateral triangle, prove that three times the square of one side is equal to
four times the square of one of its altitudes.

pls ans it's urgent​

Answer 1

Step-by-step explanation:

use Pythagoras theorem in triangle ABD in the above figure

Answer 2

Step-by-step explanation:

AD is perpendicular to BC

IN TRIANGLE ADB

ANGLE ADB=90

$ab {}^{2} = ad { }^{2} + bd {}^{2}$

AB^2=AD^2 +(BC/2)^2.....ALTITUDE OF EQUILATERAL TRIANGLE BISECTS OPPOSITE SIDE

AB^2=AD^2+BC^2/4

4AB^2=4AD^2+BC^2

4AB^2=4AD^2+AB..SIDES OF EQUILATERAL TRIANGLE ARE CONGRUENT

4AB^2-AB^2=4AD^2

3AB^2=4AD^2

HENCE PROVED

PLZ MARK AS BRAINLIEST