Question 328006
If the angles are in a ratio of 1:2:3, then let x = smallest angle.


The other angles are 2x and 3x respectively, so 
x + 2x + 3x=180
6x=180
x=30
2x=60
3x=90


This is a 30-60-90 triangle, so the sides are in a ratio of 1:2:{{{sqrt(3)}}}.


Let y= first side
2y= second side (hypotenuse of right triangle!)
{{{y*sqrt(3)}}}= third side


Perimeter={{{ y+ 2y + y*sqrt(3)=30+10*sqrt(3)}}}
{{{3y+ y*sqrt(3)= 30+ 10*sqrt(3)}}}


Therefore, y=10.

The smallest side is 10, the second side is 20, and the third side is {{{10*sqrt(3)}}}.  The perimeter checks!!


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Seminole State College of Florida
Altamonte Springs Campus