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
