Question

in an equilateral triangle prove that three times that square of one side is equal to for times the square of one off it's altitudes
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Answer 1

Let each side of the equilateral triangle be 'a' units and it's altitude be 'h' units.

To prove : - 3a² = 4h²

We know, in an equilateral triangle ,

√3/2 × a = h

On squaring both sides,

(√3/2 × a)² = (h)²

=> 3a²/4 = h²

=> 3a² = 4h²

Therefore, three times the square of any side of an equilateral triangle is equal to four times the square of its altitude.

Hence, Proved.

HOPE IT HELPS

Answer 2

plz refer to this attachment