Question

Find the altitude of an equilateral triangle whose perimeter is 18

Answer 1

Answer:

3√3 units

Step-by-step 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 ,

$\rm\implies Altitude =\dfrac{\sqrt3}{2} a$

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

$\rm\implies Altitude =\dfrac{\sqrt 3}{2} a \\\\\rm\implies Altitude =\dfrac{ \sqrt3}{2}\times 6 \\\\\rm\implies Altitude = \sqrt3 \times 3 \\\\\rm\implies\boxed{ \bf Altitude = 3\sqrt3 \ units }$