Problem 8 · 2021 Math Kangaroo
Medium
Geometry & Measurement
perimeter
A rectangle with perimeter 30 cm is divided into four parts by a vertical line and a horizontal line. One of the parts is a square of area 9 cm², as shown in the figure. What is the perimeter of rectangle ABCD?
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Answer: C — 18 cm
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Hint 1 of 2
The square has area 9, so its side is 3; the big rectangle's half-perimeter is 15.
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Hint 2 of 2
Rectangle ABCD is the big rectangle with the square's width and height removed from two sides.
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Approach: relate ABCD's sides to the whole rectangle
- The big rectangle has perimeter 30, so its length + width = 15.
- The cut-out square has side 3 (area 9), trimming 3 from one side and 3 from the other.
- Rectangle ABCD therefore has half-perimeter 15 - 3 - 3 = 9.
- Its perimeter is 2×9 = 18 cm, choice (C).
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