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Question

Find the altitude of an equilateral triangle of side 8cm.

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Solution

Let ABC be an equilateral triangle of side 8 cm i.e., AB = BC = CA = 8 cm.
Draw altitude AD which is perpendicular to BC. Then, D is the mid – point of BC.
BD=CD=12BC=82=4cm
Now, AB2=AD2+BD2 [by Pythagoras theoreum ]
(8)2=AD2+(4)2
64=AD2+16
AD2=6416=48
AD=48=43cm.
Hence, altitude of an equilateral triangle is 43cm.


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