Problem 16 · 2013 Math Kangaroo
Medium
Geometry & Measurement
areacasework
We consider rectangles that have one side of length 5.0 cm. Among them, some can be cut into a square and a rectangle, one of which has an area of 4.0 cm². How many such rectangles are there?
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Answer: D — 4
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Hint 1 of 2
Call the unknown side w; cutting off a square leaves a smaller rectangle.
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Hint 2 of 2
Set the square's area or the leftover's area equal to 4 and solve.
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Approach: case out which piece has area 4
- A 5×w rectangle cut into a square plus a rectangle: solve w²=4, (5−w)w=4, or 5(w−5)=4.
- These give w = 2, 1, 4, and 5.8 — four valid rectangles.
- So the count is 4 = D.
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