Problem 11 · 2016 Math Kangaroo
Medium
Geometry & Measurement
perimeter
Inside the square ABCD there are four identical rectangles (see diagram). The perimeter of each rectangle is 16 cm. What is the perimeter of the square?
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Answer: E — 32 cm
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Hint 1 of 2
Let a rectangle have long side a and short side b; the square's side equals a + b.
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Hint 2 of 2
Each rectangle's perimeter 2(a+b) = 16 gives a + b directly.
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Approach: relate the square side to a rectangle half-perimeter
- From the arrangement, the square's side equals one long side plus one short side, a + b.
- Each rectangle has perimeter 2(a + b) = 16 cm, so a + b = 8 cm, which is the square's side.
- The square's perimeter is 4 × 8 = 32 cm.
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