Problem 18 · 2021 Math Kangaroo
Medium
Geometry & Measurement
Algebra & Patterns
foldingarea
A rectangular strip of paper of dimensions 4 cm × 13 cm is folded as shown in the diagram. 2 rectangles are formed with areas P and Q where P = 2Q. What is the value of x?
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Answer: C — 6 cm
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Hint 1 of 2
The 45° fold makes the overlap a right-isosceles triangle, linking the two rectangle sizes.
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Hint 2 of 2
Use P = 2Q together with the strip's fixed width and length to pin down x.
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Approach: relate the two rectangle areas through the fold
- The strip has width 4, so both rectangles are 4 wide: P = 4x and Q = 4y, where x and y are their lengths.
- The 45° fold turns the strip square across its width, so the diagonal overlap uses a 4-by-4 square, and the three lengths fit the strip: x + 4 + y = 13.
- P = 2Q gives x = 2y; with x + y = 9 this makes y = 3 and x = 6.
- So x = 6 cm, the answer is C.
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