Problem 20 · 2010 Math Kangaroo
Medium
Geometry & Measurement
area-fractionfolding
A triangle is folded along the dashed line as shown. The area of the triangle is 1.5 times the area of the resulting figure. We know that the total area of the grey parts is 1. Determine the area of the starting triangle.
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Answer: B — 3
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Hint 1 of 2
Folding doubles a part onto the figure; the grey is the overlap that got covered twice.
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Hint 2 of 2
Write the folded area as the triangle minus the overlap, then use the 1.5 ratio.
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Approach: relate triangle, folded figure and overlap
- Folded figure area = triangle area T minus the overlap (the grey region).
- T = 1.5 x (folded) means folded = (2/3)T, so overlap = T - (2/3)T = (1/3)T.
- Grey = (1/3)T = 1, so T = 3.
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