Problem 19 · 2025 Math Kangaroo
Hard
Geometry & Measurement
area-decompositionsubstitution
Tim has laid out a pattern on the floor made of 11 identical tiles (see picture). How long and how wide is one of these tiles?
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Answer: B
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Hint 1 of 3
Look at one labelled side and count how many tile-lengths or tile-widths line up along it.
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Hint 2 of 3
A row of tile-widths spans one measurement, and a tile-length plus some widths spans the other - use both to pin the two sizes.
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Hint 3 of 3
Try a tile that is 4 short sides long: see if 40 cm and 10 cm rebuild both the 60 cm and 100 cm marks.
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Approach: count tile-lengths and tile-widths along the two labelled measurements
- Count along the labelled sides how many short tile-edges and long tile-edges fit; one long edge is the same as several short edges.
- Trying a long edge of 40 cm and a short edge of 10 cm, four short edges make one long edge.
- Checking the layout, these sizes rebuild both the 60 cm and 100 cm spans with all 11 tiles.
- So one tile is 10 cm wide and 40 cm long, option B.
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