Problem 11 · 2011 Math Kangaroo
Hard
Geometry & Measurement
area
A rectangle is split into three smaller rectangles. One of them measures 7 by 11 and another measures 4 by 8. Determine the measurements of the third rectangle so that its area is as large as possible.
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Answer: D — 7 by 8
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Hint 1 of 2
Imagine one rectangle filling a full side, with the remaining strip split into two.
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Hint 2 of 2
Match shared side lengths: a strip 8 wide split into a 4-tall piece leaves a 7-tall piece.
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Approach: fit shared edges to size the third piece
- Place 7×11 along the full height 11; the leftover column is 8 wide.
- Splitting that column gives the 4×8 piece and a remaining 7×8 piece.
- The largest possible third rectangle is 7 by 8.
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