Question

please give me answers fast ​

Answer 1

Step-by-step explanation:

Let, ABC be an equilateral triangle with, AB=BC=AC= x

      and AD be its altitude

WKT, in a equilateral triangle, altitude is also a median

         ∴   BD=CD= x/2

now,     ∠ADB =90°

∴By pythagoras theorem,

       AD²=AB²-BD²

              = x²-(x/2)²

              = x² -x²/4

              =(3x²)/4

  ⇒4AD²=3x²=3AB²=3BC²=3AC²

                         

                                                                            Hence  Proved

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