Problem 15 · 2021 Math Kangaroo
Medium
Geometry & Measurement
areaproportion
3 rectangles of the same height are positioned as shown. The numbers within the rectangles indicate their areas in cm². If AB = 6 cm, how long is the distance CD?
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Answer: C — 8 cm
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Hint 1 of 2
The rectangles share one height, so each width equals its area divided by that common height.
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Hint 2 of 2
AB covers the first two widths; find the height from AB, then add the last two widths for CD.
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Approach: find the shared height, then add widths
- AB spans the 12 and 18 rectangles, so (12+18)/height = 6, giving height = 5 cm.
- Then the widths are 12/5, 18/5, 22/5 = 2.4, 3.6, 4.4 cm.
- CD spans the 18 and 22 rectangles: 3.6 + 4.4 = 8 cm.
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