Question 409590


the perimeter of an equilateral triangle {{{P = 3a}}}, so


{{{32cm= 3a}}}.solve for {{{a}}}

{{{32cm/3= a}}}

{{{10.67cm= a}}}


find the length of an altitude {{{h}}} of the triangle 

imagine, you drop the {{{vertical}}}{{{ bisector}}} from the top angle down to the bottom side in your triangle

note that this bisector is also the {{{altitude}}} (height) of the triangle which equilateral triangle split in half (two right triangles)
 
so, by using the Pythagorean Theorem, we get that the length of the {{{altitude}}}

{{{h^2=a^2-(a/2)^2}}}.........plug in {{{10.67cm= a}}}

{{{h^2=(10.67cm)^2-((10.67cm)/2)^2}}}

{{{h^2=(10.67cm)^2-(5.335cm)^2}}}

{{{h^2=113.85cm^2- 28.46cm^2}}}

{{{h^2=85.39cm^2}}}

{{{h=sqrt(85.39cm^2)}}}

{{{h=9.2406709713093886351353067060983cm)}}}

{{{h=9.2cm)}}}