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MathNet 2021 — Part 08 Question 44

Math Olympiad Vault · MathNet 2021 — Part 08

Question 44

The diagonals $AC$ and $BD$ of trapezoid $ABCD$ intersect at $E$ and divide it into four triangles of areas $25\,\mathrm{cm}^2$, $36\,\mathrm{cm}^2$, $X\,\mathrm{cm}^2$, and $X\,\mathrm{cm}^2$, as shown. What is $X$?

Question illustration
  1. 25
  2. 30
  3. 32
  4. 36
  5. 61