SOLUTION: The area of a triangle is divided into 6 equal parts by line segments parallel to one side. If the length of that side is 32 cm, find the length of the longest line segment inside

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Question 1148359: The area of a triangle is divided into 6 equal parts by line segments parallel to one side. If the length of that side is 32 cm, find the length of the longest line segment inside the triangle, in cm.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The first line of the statement of the problem made it sound as if there might be an interesting problem coming.

But the rest of the statement of the problem was an extreme disappointment.

DUH! The longest line segment inside any triangle is the longest side of the triangle. Since the problem only gives the length of one of the three sides, the problem can't be solved.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

If the area of the triangle is divided by these parallel segments in 6 equal parts,


then the ratio of areas of the largest triangle to the preceding triangle is  .


If " k " is the similarity coefficient of the preceding triangle to the largest (original) triangle, then


     = ;


hence,  k = .


It implies that the length of the segment under the question is   cm.    ANSWER

Solved.


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