Question

In an equilateral triangle with side a, prove that altitude =(a root 3)/2

Answer 1

Let, ABC be an equilateral Δ, whose each side measures a units. Now draw AD ⊥ BC.

∴ The altitude and median coincide in an equilateral Δ

∴ BD = DC

⇒ BD = a/2

In right angled Δ ABD, by Pythagoras theorem,

AB² = BD² + AD²

⇒ AD² = AB² - BD²

           = (a)²- (a/2)²

           = a² - (a²/4)

          = (4a²-a²)/2

          = 3a²/2

∴ AD = 3a²/2

Hence,  altitude = 3a²/2 (is proved).

Answer 2

Step-by-step explanation:

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