Problem 23 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
pythagorean-tripleareafolding
A rectangular sheet with one side of 12 cm is folded along its 20 cm diagonal. What is the overlapping area of the folded parts, shown in gray in the picture?
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Answer: E — 75 cm²
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Hint 1 of 2
First find the rectangle’s other side from the 12 and the 20 diagonal.
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Hint 2 of 2
The overlap is an isosceles triangle; set its base on the crease and find its height.
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Approach: find the missing side, then the area of the symmetric overlap triangle
- The other side is √(20² − 12²) = 16 cm (a 12-16-20 triangle).
- Folding along the diagonal makes an isosceles overlap triangle.
- Its area is 12·(12²+16²)/(4·16) = 4800/64 = 75.
- So the overlapping area is 75 cm².
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