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+2 votes
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in Mathematics by (128k points)
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In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

2 Answers

+2 votes
by (9.9k points)
selected by
 
Best answer

 

Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC.
∴ BE = EC = BC/2 = a/2
Applying Pythagoras theorem in ΔABE, we get
AB2 = AE2 + BE2 

 

⇒ 4 × (Square of altitude) = 3 × (Square of one side)

+1 vote
by (9.9k points)

Solution: Let us assume that each side of the triangle is ‘a’, then its altitude AM is as follows:

similar triangles exercise solution

Four times of square of altitude can be calculates as follows:

similar triangles exercise solution

Hence; three times of square of a side = four times of square of altitude proved

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