Question

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

Answer 1

Answer:

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

Answer:

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Step-by-step explanation:

Let a be the side of the equilateral triangle.

∴BE=EC=2BC=2a

To prove:- 4AE2=3a2 

In △ABE, by pythagoras theorem

AB2=AE2+BE2

a2=AE2+(2a)2 

⇒AE2=a2−4a2

⇒AE2=44a2−a2

⇒AE2=43a2

⇒4AE2=3a2

Hence proved that three times the square of one side is equal to four times the square of one of its altitudes.