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MathNet 2021 — Part 01 Question 12

Math Olympiad Vault · MathNet 2021 — Part 01

Question 12

A square with side length $3$ is inscribed in an isosceles triangle with one side of the square along the base of the triangle. A square with side length $2$ has two vertices on the other square and the other two on sides of the triangle, as shown. What is the area of the triangle?
Question illustration
  1. $19\frac{1}{4}$
  2. $20\frac{1}{4}$
  3. $21\frac{3}{4}$
  4. $22\frac{1}{2}$
  5. $23\frac{3}{4}$