Problem 23 · 2010 Math Kangaroo
Stretch
Geometry & Measurement
area-fractionproportion
Lines drawn parallel to the base of the triangle pictured separate the other two sides into 10 equally large parts. What percentage of the triangle is grey?
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Answer: C — 45 %
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Hint 1 of 2
The 10 horizontal strips have areas in the ratio 1, 3, 5, 7, ... from the top.
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Hint 2 of 2
Add the shaded strips' numbers and compare to the total of 100.
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Approach: strip areas follow odd numbers
- Cutting the height into 10 equal parts makes strip areas proportional to 1,3,5,...,19 (total 100).
- The grey strips are the 1st, 3rd, 5th, 7th and 9th: 1+5+9+13+17 = 45.
- So the grey portion is 45/100 = 45%.
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