Problem 18 · 2019 Math Kangaroo
Stretch
Geometry & Measurement
perimeteroff-by-one
Anna uses 32 small grey squares to frame a 7 cm by 7 cm big picture. How many small grey squares does she have to use to frame a 10 cm by 10 cm big picture?
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Answer: C — 44
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Hint 1 of 2
The grey squares make a ring one square thick all the way around the picture.
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Hint 2 of 2
Picture the four sides of the ring, and be careful not to count the four corner squares twice.
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Approach: count the four sides of the grey ring
- Around the 7×7 picture, each side of the grey ring is 9 squares long (the 7 picture squares plus one corner at each end), and 4 sides of 9 with the 4 corners counted once give 32 — matching the picture.
- Around the 10×10 picture, each side of the ring is 12 squares long.
- Four sides of 12 is 48, but the 4 corners were each counted twice, so take 4 away: 48 − 4 = 44.
- So she needs 44 (C) grey squares.
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