in equator triangle prove that three times the square of one side is equal to four times the square of one of its altitude
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Triangle ABC is an equilateral triangle
so that AB=BC=CA
AD is the altitude of the triangle DC =1/2BC
now in triangle ADC
Ac²=AD²+DC²
AC²=ÀD²+(1/2BC²)
Ac²=AD²+1/4BC²
AC²-1/4BC²=AD²
4AC²-AC²/4=AD²
3AC²=4AD²
hence proved
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