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Question
ΔABC is am equilateral triangle of side 2a units. Find each of its altitudes.
Solution
Let AD, BE and CF be the altitudes of ΔABC meeting BC, AC and AB at D, E and F, respectively.
Then, D, E and F are the midpoint of BC, AC and AB, respectively.
In right-angled ΔABD, we have:
AB = 2a and BD = a
Applying Pythagoras theorem, we get:
`AB^2=AD^2+BD^2`
`AD^2=AB^2-BD^2=(2a)^2-a^2`
`AD^2=4a^2-a^2=3a^2`
`AD=sqrt3a units`
Similarly,
`BE=asqrt3 unit and CF=a sqrt3 unitst`
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