Question.
In an equailateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
In an equailateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
Solution:
Altitude of equilateral $\Delta=\frac{\sqrt{3}}{2}$ side
$h=\frac{\sqrt{3}}{2} a$
$h^{2}=\frac{3}{4} a^{2}$
$4 h^{2}=3 a^{2}$
Altitude of equilateral $\Delta=\frac{\sqrt{3}}{2}$ side
$h=\frac{\sqrt{3}}{2} a$
$h^{2}=\frac{3}{4} a^{2}$
$4 h^{2}=3 a^{2}$