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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The area of a square is six times the area of a rectangle with a length half that of the square and a width 6 cm less than the width of the square. What is the perimeter of the square?

(A) $24\text{ cm}$ (B) $28\text{ cm}$ (C) $32\text{ cm}$ (D) $36\text{ cm}$ (E) $40\text{ cm}$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.