Problem 15 · 2019 Math Kangaroo
Hard
Geometry & Measurement
ratioarea
The flag of Kanguria is a rectangle whose side lengths are in the ratio 3 : 5. The flag is split into four rectangles of equal area, as shown. In which ratio are the side lengths of the white rectangle?
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Answer: E — 4 : 15
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Hint 1 of 2
The flag splits into four equal-area rectangles: one tall left strip plus three stacked bars on the right.
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Hint 2 of 2
Use the 3:5 side ratio to size the white bar, then take its own width-to-height ratio.
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Approach: size the pieces from equal areas
- Take the flag 5 wide by 3 tall; each of the four equal pieces has area 15/4.
- The left strip is 5/4 × 3; the three right bars are each 15/4 wide by 1 tall.
- The white bar is 1 by 15/4, side ratio 1 : 15/4 = 4 : 15.
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