Question

ABC is equilateral triangle of side 2a then the length of one of its altitude is​

Answer 1

Answer:

√3a units

Step-by-step explanation:

We know that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

In the equilateral ΔABC, we see that AB = BC = CA = 2a [From the figure shown above]

AD ⊥ BC [Construction]

⇒ BD = CD = 1/2 BC = a [Since the perpendicular drawn from a vertex to the opposite side bisects the opposite side in an equilateral triangle]

In ΔADB, using pythagoras theorem,

AB2 = AD2 + BD2

AD2 = AB2 - BD2

AD2 = (2a)2 - a2

AD2 = 4a2 - a2

AD2 = 3a2

AD = 3a

⇒ AD = √3a units

Similarly, we can prove that, BE = CF = √3a units

Summary:

If ABC is an equilateral triangle of side 2a, then each of its altitudes are AD = BE = CF = √3a units.