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Let the altitude be L units
side be A units
to prove , 3A² = 4L²
since the altitude perpendicularly divides the side into two equal parts 
so, by Pythagores theorem.
altitude, L² = (A² - (A/2)²)
                  = A²- A²/4
by cross multiplication, 
4L² = 3A² proved 

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