Question

In an equilateral triangle, prove that three
time the square of one side is equal to
four time the square of one of it altitudes
​

Answer 1

Answer:

Let each side of the equilateral triangle be 'a' units and it's altitude be 'h' units. Therefore, three times the square of any side of an equilateral triangle is equal to four times the square of its altitude. Hence, Proved.

Answer 2

given :

In an equilateral triangle

To prove :

that three time the square of one side is equal to four time the square of one of it altitudes

Solution :

In ΔABC, AD perpendicular BC

Also, AB = BC = CA. ...(i)

As AD perpendicular BC, altitude AD will bisect BC

so that,

BD = CD = ½ BC ..(ii)

Now, in right Δ ADB, ∠ADB = 90°

AB² = AD² + BD²

AB²-AD²(½Bc)².....[Using (ii)]

AB² = AD² +¼AB².......[Using (i)]

4AB² = 4AD² + AB²

3AB² = 4AD²