ABC is an equilateral triangle of side 3a find each of its altitude
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Step-by-step explanation:
in an equilateral triangle the altitude from a vertex bisects it's opposite side.
If ABC is the equilateral ∆ and AD | BC then AD bisects BC
AB=BC=CA=3a
therefore by Pythagoras theorem
AB^2 = DC^2 + AD^2
==> AD^2 = AB^2 -DC^2
==> AD^2 = AB^2 - (BC/2)^2
==> AD= √[(3a)^2 - (3a/2)^2]
==> AD = √[9a^2 - 9a^2/4 ]
==> AD = √[27a^2/4]
==> AD = 3√3a/4
Also in an equilateral triangle all altitudes are equal. so all attitude are of length 3√3a/4
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