SOLUTION: The area of triangle ABC is trisected by two segments parallel to base BC. The longer of these segments is 24 cm. What is the length of base BC? Express your answer in simplest rad

Question 1027688: The area of triangle ABC is trisected by two segments parallel to base BC. The longer of these segments is 24 cm. What is the length of base BC? Express your answer in simplest radical form.
Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
The area of triangle ABC is trisected by two segments parallel to base BC. The longer of these segments is 24 cm. What is the length of base BC? Express your answer in simplest radical form.
Triangle ABC znd triangle AFG are similar
Triangle ABC /triangle AFG = BC^2/FG^2
3/2 = BC^2/FG^2
3/2 = BC^2/12^2
BC^2= 3/2 * 12^2
BC = sqrt( 3/2*12^2)
BC = 12sqrt(6)

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Let the longer segment be CD.

Triangles ACD and ABC are similar.

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.

By a very powerful general principle regarding similar figures, the ratio of linear measurements between triangle ACD and triangle ABC is .

So the length of BC is

ANSWER:

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