Two squares are placed partly overlapping, forming eight non-overlap triangles. Two triangles have a pink and two have a yellow perimeter. What is pink : yellow?
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Solution
Pink : yellow is 1 : 1.
Solution by Marshall W. Buck: The yellow and pink triangles are all similar right triangles, so the perimeters are proportional to their altitudes from their right corners. The sum of the two yellow altitudes plus the width of their base square will be equal to the width of the other square in the x-direction. The height of that other square in the y-direction is the same as its width, so the sum of the altitudes of the pink triangles will be the same, and therefore the sum of the pink perimeters equals the sum of the yellow perimeters.
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