Question

The area of an equilateral triangle is
16√3 cm? then its attitude is ​

Answer 1

Let the triangle be ABC and altitude be AD.

Since altitude divides the triangle in two equal parts.

So, by Pythagoras theorem. In triangle ABD

$(ad) {}^{2} = (ab) ^{2} + (bd) {}^{2}$

$(ad) { }^{2} =( ab) {}^{2} + ( \frac{bd}{2} ) {}^{2}$

$(ad) { }^{2} = (6 \sqrt{2} ) { }^{2} + ( \frac{6 \sqrt{2} }{2} ) {}^{2}$

$( ad) {}^{2} = 72 + \frac{72}{2}$

$(ad) {}^{2} = 72 + 36$

$ad = \sqrt{72 + 36}$

$ad = \sqrt{108}$

Or,

$ad = 10.39$