The length of the side of an equilateral triangle is \(4\sqrt{3}\) cm. Find its height.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6 cm
The height of an equilateral triangle falls on the midpoint of the base and cuts the triangle into two right triangles, so Pythagoras gives the height: \(\displaystyle h=\frac{\sqrt{3}}{2}a\).
Half the base \(=2\sqrt{3}\) cm
In the right triangle formed by the height: \(h^2=(4\sqrt{3})^2-(2\sqrt{3})^2=48-12=36\)
\(h=6\) cm
