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2018 Math Kangaroo

Problem 9

Problem 9 · 2018 Math Kangaroo Medium
Geometry & Measurement factorization

The faces of the brick have areas A, B and C, as shown. How big is the volume of the brick?

Figure for Math Kangaroo 2018 Problem 9
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Answer: B — \(\sqrt{ABC}\)
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Hint 1 of 2
Call the edge lengths x, y, z and write A, B, C in terms of them.
Still stuck? Show hint 2 →
Hint 2 of 2
Multiply the three face areas and see what comes out.
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Approach: multiply the three face areas to recover the volume
  1. With edges x, y, z the faces have areas A=xy, B=yz, C=zx.
  2. Then ABC = (xyz)², so xyz = √(ABC).
  3. The volume is xyz = √(ABC).
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