Question

The perimeter of an equilateral triangle is 45 centimeters. How do you find the length of an altitude of the triangle?

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`