Question

22. In an equilateral triangle, prove that three times th
square of one side is equal to four times the square
one of its altitudes.
[NCERT EXERCIS​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

Let is the length of the side of equilateral triangle - a and AE - altitude.

So BE = EC = BC/2 = a/2

In triangle ABC,  From Pythagoras Theorem

AB2 = AE2 + BE2

=> a2 = AE2 + (a/2)2

=> AE2 = a2 - a2 /4

=> AE2 = 3a2 /4

=> 4AE2 = 3a2

=> 4*(square of altitude) = 3*(square of one side)

So three times the square of one side is equal to four times the square of one of its altitudes.

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