Problem 8 · 2016 Math Kangaroo
Medium
Geometry & Measurement
areaproportion
The rectangles S1 and S2 shown in the picture have the same area. Determine the ratio x : y.
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Answer: E — 8:5
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Hint 1 of 2
Write each rectangle's area from the lengths shown in the picture.
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Hint 2 of 2
Set the two areas equal and solve for x:y.
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Approach: equal-area condition from the figure
- From the diagram the two rectangles share the same area while one is short and tall and the other long and short.
- Setting their areas equal and simplifying the proportion gives x:y = 8:5.
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