IMC 2009 Q20
20. A square, of side two units, is folded in half to form a triangle. A second fold is made, parallel to the first, so that the apex of this triangle folds onto a point on its base, thereby forming an isosceles trapezium. What is the perimeter of this trapezium?
- A \(4 + \sqrt{2}\)
- B \(4 + 2\sqrt{2}\)
- C \(3 + 2\sqrt{2}\)
- D \(2 + 3\sqrt{2}\)
- E 5
Intermediate Mathematical Challenge 2009, Question 20. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(2 + 3\sqrt{2}\)
As can be seen from the figures below, the perimeter of the trapezium is \(2 + 3\sqrt{2}\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.