Question

An equilateral ∆ has sides of length 16 cm. Find the length of an altitude.

Answer 1

The length of the altitude is $8\sqrt{3}$

Explanation:

Let ABC be an equilateral triangle.

It has sides of length 16 cm

Let AD be the altitude of the triangle.

We need to determine the length of an altitude.

Let AC = 16 cm and CD = 8 cm

Let us consider the right angled triangle ADC

Using the Pythagorean theorem, we have,

$AC^2=AD^2+DC^2$

Substituting the values, we get,

 $16^2=AD^2+8^2$

 $256=AD^2+64$

 $192=AD^2$

$8\sqrt{3}=AD$

The length of the altitude is $8\sqrt{3}$