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UKMT Senior Mathematical Challenge, 2020

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

Two congruent pentagons are each formed by removing a right-angled isosceles triangle from a square of side-length 1. The two pentagons are then fitted together as shown. What is the length of the perimeter of the octagon formed?

(A) $4$ (B) $4 + 2\sqrt{2}$ (C) $5$ (D) $6 - 2\sqrt{2}$ (E) $6$

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