Problem 11 · 2023 Math Kangaroo
Medium
Geometry & Measurement
perimetergrid
A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of 80 cm. A snake lies along the edges of the tiles (see picture). How long is the snake?
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Answer: C — 420 cm
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Hint 1 of 3
A square's perimeter is four equal sides, so first turn the 80 cm into the length of one small-tile side.
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Hint 2 of 3
Use that small side as your ruler and walk along the snake, counting how many small sides fit into each straight stretch.
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Hint 3 of 3
Add up all the little side-lengths the snake covers, then multiply by the length of one side.
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Approach: find the small-tile side, then count how many of those lengths the snake covers
- The smallest tile is a square with perimeter 80 cm, so each of its sides is 80 / 4 = 20 cm.
- Reading the snake's path along the tile edges, it stretches across 21 of these small side-lengths.
- So the snake is 21 × 20 cm = 420 cm long.
- The answer is C, 420 cm.
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