Problem 1 · 2019 Math Kangaroo
Medium
Geometry & Measurement
ratioarea
The flag of Kangoraland is a rectangle split into three equal rectangles, as shown. What is the ratio of the side lengths of the white rectangle?
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Answer: A — 1 : 2
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Hint 1 of 2
The three rectangles are congruent — the tall dark one is just one of them stood on end.
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Hint 2 of 2
Give the small rectangle sides 1 and 2 and check that one upright plus two stacked sideways tile the flag.
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Approach: the three congruent rectangles are one upright beside two stacked sideways
- Let each of the three equal rectangles have short side 1 and long side r.
- The dark rectangle stands upright (width 1, height r); the grey and white rectangles lie sideways (width r, height 1) and are stacked, so together they are r wide and 2 tall.
- For the flag to be a rectangle, the upright height must equal the stacked height: r = 2.
- So each rectangle is 1 by 2, and the white rectangle's sides are in ratio (A) 1 : 2.
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