Question

The altitude of an equilateral triangle is 9 inches. Find the perimeter of the triangle in inches.

Answer 1

If we  draw a perpendicular line from one of the vertices of the triangle we get  2 right angled triangles  each with  altitude 9 ins  and vertex angle = 30 degrees.   So:-

cos 30 = 9 /h     where h = one of the sides of the equilateral triangle

h =  9 / cos 30  =  10.392 inches

Therefore the perimeter of the triangle = 3 * 10.392 =  31.1769 ins

Answer is 31.18 inches to the nearest hundredth.