Question 1189247
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Here is a figure.  Use the ratio {{{1}}}:{{{sqrt(3)}}}:{{{2}}} for the side lengths of a 30-60-90 right triangle to find the lengths of the sides of triangle ABC.<br>
{{{drawing(300,400,-2,10,-1,15
,line(0,0,8,0),line(0,0,0,13.856),line(8,0,0,13.856),line(0,0,6,3.464)
,locate(0,-.5,C),locate(8,-.5,A),locate(0,15,B),locate(6,4.5,D)
,locate(2,0.75,30),locate(4,-.5,8),locate(5,4,90)
)}}}<br>
(1) In triangle ADC, use AC=8 and ACD=30 degrees to determine AD and DC.
(2) In triangle CDB, use CD from (1) and angle BCD=60 degrees to determine AB and BD.<br>
Your final answer for the perimeter of triangle ABC should be {{{24+8sqrt(3)}}}<br>