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IMSO 2009 Mathematics Contest in Taiwan – Short Answer Question 10

IMSO Maths · IMSO 2009 Mathematics Contest in Taiwan – Short Answer

Question 10

I have a rectangular picture whose edges are each an exact number of centimetres in length. At a quick glance it could be mistaken for a square, but it is not a square. It is placed inside a black border which is 3 cm wide all the way around. The area of the border is exactly equal to the area of the picture. What is the area, in $\text{cm}^2$, of the picture alone?

Question illustration