Question 1146136
1. The volume of a regular triangular prism is 240 square root of 3 cu
In. and its altitude is 15 in.
 Find the side of the base
:
Assuming the base triangle is a equilateral triangle
let s = the side of the base
Find the height of the base triangle
h = {{{sqrt(s^2-(.5s)^2)}}}
h = {{{sqrt(s^2-.25s^2)}}}
h = {{{sqrt(.75s^2)}}}
Find the area of the base triangle
A = {{{1/2}}}s*h
Replace h
A = {{{1/2}}}{{{s*sqrt(.75s^2)}}}
extract s
A = {{{1/2}}}{{{s^2*sqrt(.75)}}}
volume (240) is the area of the base * the altitude (15)
{{{1/2}}}{{{s^2*sqrt(.75)*15}}} = {{{240sqrt(3)}}}
get rid of the fraction, mult by 2
{{{s^2*sqrt(.75)*15}}} = {{{480sqrt(3)}}}
divide both sides by 15
{{{s^2*sqrt(.75)}}} = {{{32sqrt(3)}}}
square both sides
{{{s^4*.75}}} = 1024*3
{{{s^4*.75}}} = 3072
divide both sides by .75
{{{s^4}}} = 4096
Use your calc to find the 4th root of 4096
s = 8 inches is the side of the base