Question

prove that three times the square of any side of an equilaterial
triangle is equal to four time the square of the altitude ​

Answer 1

HEY MATE YOUR ANSWER IS HERE

FIGURE - ( GIVEN IN ATTACHMENT )

TO PROVE - three times the square of any side of an equilaterial

three times the square of any side of an equilaterialtriangle is equal to four time the square of the altitude

GIVEN - in the figure triangle is equilateral hence

AB = BC = AC , AND BM = MC

PROOF

IN triangle ABC let AB = BC= AC = 2a

now in triangle ABM

AB ² = AM ² + MC ²

now

(2a)² = (2a/2)² + AM² [ MC = BM , MC + BM =

2 MC = BC ]

( HENCE MC = BC/2 = 2a/2 )

4a² - a² = AM²

3a² = AM ²---------eq 1

NOW,

side² = (2a)²=4a² ----eq2

AM ² = 3a²--------eq 3

according to eq 2 and 3

three times the square of any side of an equilaterial

three times the square of any side of an equilaterialtriangle is equal to four time the square of the altitude

3(side ²) = 4( AM ² )

3( 4a² ) = 4 ( 3a² )

12a² = 12a²

HENCE PROVED ...

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