Question 1159252

the height divides an equilateral triangle into two congruent right triangles where the height and {{{1/2}}} of side are legs and the length of hypotenuse is equal to the length of side

using Pythagorean theorem, we have

{{{h^2= 36^2-(36/2)^2}}} 
 
{{{h^2= 1296-324}}} 

{{{h^2= 972}}} 

{{{h= sqrt(972)}}} 

{{{h= 18sqrt(3)}}} 

{{{h=31.2}}} inches


answer is: D. {{{31.2in}}}