Problem 18 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
areapythagorean-triple
A large square touches two other squares, as shown. The numbers inside the smaller squares give their areas. What is the area of the largest square?
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Answer: D — 13
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Hint 1 of 2
Set the tilted big square against the two small ones and look at right triangles.
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Hint 2 of 2
The big square's side splits into pieces tied to sides 3 and 2.
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Approach: Pythagorean relation from the touching configuration
- The small squares have sides 3 and 2 (areas 9 and 4).
- The way the large square leans on them makes its side the hypotenuse of a right triangle with legs 3 and 2.
- So its area = 3² + 2² = 13.
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