Problem 12 · 2024 Math Kangaroo
Stretch
Geometry & Measurement
areaperimeter
Christian cuts four small grey squares out of one big square. The white shape remains (see picture). This shape has half the area of the big square. The side lengths of the small grey squares are given in the drawing. What is the perimeter of the white shape?
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Answer: B — 40
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Hint 1 of 2
First use the 'half the area' fact: the four grey squares together equal half the big square, which pins down the big square's side.
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Hint 2 of 2
Cutting a square notch out of a corner does not change the perimeter, because the two removed edges are replaced by two equal new edges.
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Approach: find the side from areas, then note corner notches keep the perimeter
- The grey squares have areas 1, 4, 9 and 36, summing to 50, and this is half the big square, so the big square has area 100 and side 10.
- Removing a square from a corner trades two outer edges for two new inner edges of equal length, so the perimeter is unchanged.
- Hence the white shape has the same perimeter as the big square: 4 × 10 = 40.
- The perimeter of the white shape is 40.
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