Question

Find the perimeter of an equilateral triangle that has a side measure of 45 cm.

Answer 1

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