Problem 16 · 2014 Math Kangaroo
Medium
Geometry & Measurement
work-backward
The points A, B, C, D, E, F lie on a straight line in this order. These distances are known: AF = 35, AC = 12, BD = 11, CE = 12, and DF = 16. How long is BE?
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Answer: D — 16
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Hint 1 of 2
Put A at 0 and F at 35, then place the other points using the given distances.
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Hint 2 of 2
Once every point has a position on the line, BE is just the difference of E's and B's positions.
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Approach: give each point a coordinate on the line, then subtract
- Set A = 0, so F = 35. Then C = 12 (from AC = 12).
- DF = 16 puts D at 35 − 16 = 19, and BD = 11 puts B at 19 − 11 = 8.
- CE = 12 puts E at 12 + 12 = 24.
- So BE = 24 − 8 = 16.
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