The perimeter of an equilateral triangle is 45 centimetersFind the length of an altitude?

Each side of the triangle is 45cm/3=15cm. The altitude divides the base into two equal segments of 7.5cm. This results in a right triangle with hypotenuse 15 cm and base 7.5cm. Pythagorus tells us a2+b2=c2 where a=altitude, b=base, c=hypotenuse. a2=c2-b2=152-7.52=225-56.25=168.75, a=12.99cm. Alternatively, the 3 angles of an equilateral triangle are all 60 degrees. The altitude divides one of these angles into two 30 degree angles. The cosine of 30 degrees is the opposite divided by the adjacent side. The adjacent side is the altitude. Thus a/c=cosine of 30 degrees, a=c X cos30 degrees = 15X0.866=12.99cm