ABC is an equilateral triangle of side 3a find each of its altitude

1.	ABC is an equilateral triangle of side 3a find each of its altitude
Answer» 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

Answer»

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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