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 1

Answer:

Step-by-step explanation:

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.

Answer 2

Answer:3a square = 4AD

Step-by-step explanation:

ABD is right angled triangle

Using P.T.

Hypotenuse=(height)sq.+ (base)sq.

AB= AD sq.+ BD sq.

a sq.= AD sq.+(1/2a)sq.

4a sq.-a sq./4 = AD sq.

3a sq. = 4 AD