Question

In an equilateral triangle of side 2a, calculate it's altitude. (using heron's formula)​

Answer 1

In the above figure,

ABC is an equilateral triangle.

AD is its altitude

In ∆ADB,

angle D is 90° i.e,

∆ADB is a right angled triangle.

In a right angled triangle, according to Pythagoras theorem,

(AB)^2 = (AD)^2 + (BD)^2

(2a)^2 = (AD)^2 + (2a/2)^2

4a^2 = (AD)^2 + a^2

AD = √3a

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