Find the altitude of an equilateral triangle that has a perimeter of 18 inches

Find the altitude of an equilateral triangle
that has a perimeter of 18 inches?
altitude
= sqrt (6^2 - 3^2)
= sqrt 27
= 3 sqrt 3

Perimeter = 18 in
each side = 6 in
The altitude of an equilateral triangle divides the triangle into 2 30 - 60 rt triangles, each with a base = 3 in
If the hypotenuse of a 30 - 60 rt triangle is 6, what is the length of the longer leg 6(√(3)/2) = 3√3 in

or use pythagorean theorem to prove this also with the base = 3 in and the hypotenuse = 6 in

Side length = 18/3 = 6

Drop perpendicular from one vertex to opposite side
We now have 2 right triangles with base = 3 and hypotenuse = 6

Altitude = √(6²−3²) = √(36−9) = √27 = 3√3