Question

What is the length to the nearest tenth of the altitude of an equilateral triangle with a perimeter of 30 inches

Answer 1

Each side of an equilateral triangle = perimeter / 3.
Each side = 10 inches.
The altitude divides the triangle into two 30 60 90 triangles.  The hypotenuse is 10 inches and the short side is 5 inches.
altitude^2 = 10^2 - 5^2
altitude^2 = 100 - 25
altitude^2 = 75
altitude = 8.6602540378