Find the perimeter of an equilateral triangle that has a side measure of

45 cm.

A triangle with 45 cm of perimeter has 15 cm of side. The

"altitude" connects the middle of one side to the opposite vertice. This forms a rectangle triangle with hypothenuse 15 cm and the small catet a = 7.5 cm. So by the Pythagoras theorem we must solve the equation:

7.5^2+b^2=15^2

b=sqrt (225-56.25) = sqrt (168.75) = 12.99 cm

Other solution was using trigonometry:

b / (side) = sin (pi/3) = sqrt (3) / 2

b=7.5*sqrt (3) / 2=12.99 cm