Question 1027688
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Let the longer segment be CD.<br>
Triangles ACD and ABC are similar.<br>
Since the area of triangle ABC is divided into three equal parts by the two segments parallel to BC, the ratio of the area of triangle ACD to the area of triangle ABC is 2:3.<br>
By a very powerful general principle regarding similar figures, the ratio of linear measurements between triangle ACD and triangle ABC is {{{sqrt(2):sqrt(3)}}}.<br>
So the length of BC is {{{((sqrt(3)/sqrt(2)))(24)=((sqrt(6)/2))(24)=12sqrt(6)}}}<br>
ANSWER: {{{12sqrt(6)}}}<br>