Question

In an equilateral triangles prove that three lines the square of one side is equal to four times square of one of its altitude

Answer 1

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

Answer 2

plz refer to this attachment