Question:
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.
Answer:
Let a is the length of the side of equilateral triangle and AE is the altitude.
So BE = EC = BC/2 = a/2
Now 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.
Not what you are looking for? Go ahead and submit the question, we will get back to you.
