Problem 29 · 2011 Math Kangaroo
Stretch
Geometry & Measurement
area-decompositionpaper-cutting
The figure on the left consists of two rectangles. Two side lengths are marked: 11 and 13. The figure is cut into three parts along the two lines drawn inside. These can be put together to make the triangle shown on the right. How long is the side marked x?
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Answer: B — 37
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Hint 1 of 2
Cutting and rearranging does not change total area — set rectangle area equal to triangle area.
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Hint 2 of 2
Use the marks 11 and 13 to find the area, then solve for the side x.
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Approach: the two rectangles' area equals the triangle's area
- The three cut pieces from the two rectangles reassemble into the triangle, so the total area is preserved.
- Using the marked lengths 11 and 13 to compute that area and matching it to the triangle gives the missing side.
- Solving for x yields 37.
Mark:
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