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Question
Find the height of an equilateral triangle of side 12cm.
Solution
Let ABC be the equilateral triangle with AD as an altitude from A meeting BC at D. Then, D will be the midpoint of BC.
Applying Pythagoras theorem in right-angled triangle ABD, we get:
`AB^2=AD^2+BD^2`
`⇒ AD^2=12^2-6^2(∵BD=1/2 BC=6)`
`⇒AD^2=144-36=108`
`⇒AD=sqrt108=6sqrt3 cm`
Hence, the height of the given triangle is `6sqrt3` cm.
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