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Question

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

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Solution

We have the length of each side = 12cm
Therefore the altitude bisects the side on which it stands into 2 equals each measuring 6cm
Hence one half of the triangle being a right angled triangle will have the following measurements
Hypotenus = side of the triangle = 12cm
Base= half of the side on which the altitude stands = 6 cm
Therefore as per the Pythagoras theorem
Altitude+%5E2+=+Hypotenuse%5E2+-+Base%5E2
= 12%5E2+-+6%5E2
= 144+-+36
= 108
Therefor the Altitude = %28108%29%5E%281%2F2%29
= 6%5E%281%2F3%29


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