Problem 1 · 2017 Math Kangaroo
Easy
Geometry & Measurement
area-fractionsymmetry
The diagram shows an isosceles triangle, where the height is marked and its area is split up into equally wide white and grey stripes. Which fraction of the area of the triangle is white?
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Answer: A — 12
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Hint 1 of 2
The height line splits the triangle into a left and right half — compare a grey stripe with the white stripe right next to it.
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Hint 2 of 2
By the symmetry of the picture, each grey region can be paired with an equal white region.
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Approach: pair equal regions by symmetry
- The triangle is cut into equal-width horizontal stripes, and the marked height splits it down the middle.
- On one side the stripes are white where the other side is grey, so each grey patch is matched by an equal-area white patch.
- The white and grey areas are therefore equal, so the white part is 1/2 of the triangle.
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