Question

the side of an equilateral triangle are8 units long. what is the length of the altitude of the triangle?

Answer 1

So, the triangle is equilateral, all its sides are equal⇒

AB=BC=AC=8

In an equilateral triangle, the height is also the median, so it divides the sides into 2 equal parts⇒

AO=OC=8:2=4

by the Pythagorean theorem

$8^2=4^2+BO^2\\BO^2=64-16\\BO=\sqrt{48} \\BO=4\sqrt{3}$

Answer: BO=4√3

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