Question

DMARKS WUBOTU
1.
Prove that three times the square of any side
an equilateral triangle is equal to four times
the square of an altitude.​

Answer 1

1. let ABC an equilateral triangle , let the side of the equilateral triangle be considered as 'a'
2. And AE the altitude of the triangle therefore BC = AC = BC /2 = a/2
3. Applying Pythagoras theorem in triangle ABC get: AB^2=AE^2+BE^2 =
4. a^2=AE^2+(a/2)^2
5. AE^2=a^2-a^2/4
6. AE^2=3a^2/4
7. 4AE^2=3a^2