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UKMT Senior Mathematical Challenge, 2020

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A square with perimeter 4 cm can be cut into two congruent right-angled triangles and two congruent trapezia as shown in the first diagram in such a way that the four pieces can be rearranged to form the rectangle shown in the second diagram. What is the perimeter, in centimetres, of this rectangle?

(A) $2\sqrt{5}$ (B) $4\sqrt{2}$ (C) $5$ (D) $4\sqrt{3}$ (E) $3\sqrt{7}$

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