Problem 23 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
Number Theory
areaperfect-square
Sofia has 52 isosceles right triangles, each of area 1 cm². She wants to make a square using some of these triangles. What is the area of the largest square she can make?
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Answer: D — 50 cm²
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Hint 1 of 2
Each triangle has area 1, so a square built from k of them has area k.
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Hint 2 of 2
Right isosceles triangles assemble into squares whose area is twice a perfect square (2, 8, 18, 32, 50, ...).
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Approach: find the largest valid square area within the supply
- Each triangle has area 1, so a square of these has an integer area equal to the number used.
- These isosceles right triangles tile squares of area 2×1², 2×2², 2×3², ... = 2, 8, 18, 32, 50.
- The largest such area not exceeding 52 triangles is 50.
- So the biggest square is 50 cm², choice D.
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