Question

16. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes. ​

Answer 1

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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

Step-by-step explanation:

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