Problem 21 · 2010 Math Kangaroo
Stretch
Geometry & Measurement
area-fraction
Lines drawn parallel to the base of the triangle pictured separate the two other sides into 10 equal-sized parts. What percentage of the triangle is grey?
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Answer: B — 45 %
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Hint 1 of 2
Strips cut parallel to the base have areas like 1, 3, 5, 7, ... from the top.
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Hint 2 of 2
Add up only the grey strips and compare with the total of 100.
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Approach: strip areas are consecutive odd numbers
- From the apex the strips have areas 1, 3, 5, ..., 19, totalling 100 parts.
- The grey strips are the odd-positioned ones: 1 + 5 + 9 + 13 + 17 = 45 parts.
- So the grey region is 45 % of the triangle.
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