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In an equilateral triangle prove that three times the square of one side is equal to four times the square of its altitude?
Most Upvoted Answer
In an equilateral triangle prove that three times the square of one si...
Hey, here is your answer ....

(1) PHELA TARIKA :-

Let ABC be equilateral triangle.

Let AD be perpendicular bisector from A on to BC. So BD = CD = 1/2 BC

ADC is a right angle triangle. So  AC² = AD² + DC²
AC² = AD² + (1/2 AC)²           

    AD² = 3/4 AC²  

     4 AD² = 3 AC²


(2) DOOSRA TARIKA :-

Draw AD PERPENDICULAR to BC.

sin60 = AD/AB
Squaring both sides,

sin²60 = AD²/AB²

3/4=AD²/BD²


3AB²=4AD²

Hence, proved....
Community Answer
In an equilateral triangle prove that three times the square of one si...
Let a is the length of the side of equilateral triangle and AE is the altitude.

So BE = EC = BC/2 = a/2

Now in triangle ABC,

From Pythagoras Theorem

AB2 = AE2 + BE2

=> a2 = AE2 + (a/2)2

=> AE2 = a2 - a2 /4

=> AE2 = 3a2 /4

=> 4AE2 = 3a2

=> 4*(square of altitude) = 3*(square of one side)

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