In an equilateral triangle, prove that three times the square of the one side is equal to four times the square of one of its altitude.
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Given,
- ΔABC is an Equilateral triangle .
To Prove :
- 4 x (square of altitude ) = 3 x ( Square of one side ).
Proof :
Let the Side of Equilateral triangle be a
And , AD is an altitude of ΔABC .
∴BD = DC = =
Now Applying Pythagoras Theorem in ΔABC :
[ So here 4 times of square altitude = 3 times of square of one side ]
Hence Proved
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