Problem 16 · 2024 Math Kangaroo
Medium
Geometry & Measurement
substitution
A kitchen floor uses two kinds of tiles: long rectangles and small squares. The picture shows part of the floor. Each rectangular tile is 23 cm long and 11 cm wide. How long is one side of a small square tile?
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Answer: D — 6 cm
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Hint 1 of 2
Look at one straight line in the weave where a rectangle's length lines up with its width plus some squares.
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Hint 2 of 2
Set up: 23 = 11 + (two square sides) and solve for one side.
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Approach: match lengths along the basket-weave edges
- In the weave, a rectangle's long side (23) equals its short side (11) plus two small-square sides.
- So 23 = 11 + 2 × (square side).
- Then 2 × (square side) = 12, giving a square side of 6.
- Answer: 6 cm (D).
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