Question

Find the altitude of an equilateral triangle whose perimeter is 18

Answer 1

3√3 units

Explanation:

We are asked to find the altitude of the equilateral triangle whose perimeter is 18 . Firstly let us find the side of the∆.

`\rm \implies a + a + a = 18 \\\\\rm\implies 3a = 18 \\\\\rm\implies a = 6`

Now we know that in a equilateral triangle , the altitude of the triangle with side length a is ,

`\rm\implies Altitude =(\sqrt3)/(2) a`

Plug in the value of a that is 6 , we will get ,

`\rm\implies Altitude =(\sqrt 3)/(2) a \\\\\rm\implies Altitude =( \sqrt3)/(2)* 6 \\\\\rm\implies Altitude = \sqrt3 * 3 \\\\\rm\implies\boxed{ \bf Altitude = 3\sqrt3 \ units }`