Due December 13

This problem is best solved by working out examples. We consider this to be a medium problem, worth 15 points. Send answers and questions to mathstat@uoguelph.ca

Suppose we have a rectangle like the one shown below, which is to be cut in half. If the short side has a length of one unit, what length for the long side will make the two half rectangles exactly the same shape as the original rectangle? By same shape we mean that the ratio of the long side to the short side is the same. For full marks, your answer should not be a decimal approximation like 1.5 or 3.14 but an exact mathematical expression.

Hint: the answer involves a square root which you can e-mail as SQRT. So if the answer were three plus the square root of seven you could e-mail me 3+SQRT(7). You can also e-mail me a scan of your work.

Send your answer to mathstat@uoguelph.ca

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