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MathNet 2013 Question 33

Math Olympiad Vault · MathNet 2013

Question 33

The figure contains a square and two congruent right triangles.
Question illustration
These polygons form a rectangle and a trapezoid as shown next:
Question illustration
Given that the rectangle's perimeter is $58$ and the trapezoid's perimeter is $60$, calculate the side of the square.
Note: A right triangle has an angle of $90^\circ$. Two triangles are congruent when their corresponding sides have equal lengths.