Question 939987

An equilateral triangle has {{{3}}} equal sides.

If each side is {{{a}}} and a height is {{{h}}}, we know that {{{h}}} divides equilateral triangle into two right triangles with legs {{{h}}} and {{{a/2}}}, and hypotenuse {{{a}}}.

use Pythagoras theorem to find {{{a}}} when {{{h=18cm}}} 

{{{a^2=(a/2)^2+h^2}}}

{{{a^2-(a/2)^2=(18cm)^2}}}


{{{a^2-a^2/4=324cm^2}}}


{{{4a^2/4-a^2/4=324cm^2}}}


{{{3a^2/4=324cm^2}}}


{{{3a^2=1296cm^2}}}


{{{a^2=1296cm^2/3}}}


{{{a^2=432cm^2}}}


{{{a=sqrt(432cm^2)}}}

{{{a=sqrt(3*144cm^2)}}}

{{{a=12sqrt(3)cm}}}


then the exact perimeter is:

{{{P=3a}}}

{{{P=3*12sqrt(3)cm}}}

{{{P=36sqrt(3)cm}}}