Question

in equilateral triangle prove that three times the square of one side is equal to four times the square of one of its altitude.​

Answer 1

Hello mate here's ur answer

let ABC be an equilateral triangle of side a

draw a median AD from A to side BC.

Now, BD=CD= a/2

from ADC,

LADC=90°

AC=a

DC=a/2

according to pythogoras theorem ,

${hyp}^{2} = {side }^{2} + {side }^{2} \\ so \\ {ac}^{2} = {ad}^{2} + {dc}^{2} \\ {a}^{2} = {x}^{2} + { \binom{a}{2} }^{2} \\ {x}^{2} = {a}^{2} - { \frac{a}{4} }^{2} \\ {x}^{2} = \frac{4 {a}^{2} - {a}^{2} }{4} \\ {x}^{2} = \frac{3 {a}^{2} }{4} \\ 4 {x }^{2} = 3 {a}^{2}$

hence proved !!