If an A4 sheet is cut exactly in half along a line parallel to the shorter side, two sheets are created that have the same shape as the original one, that is, they are obtained from it by a rotation and a scaling. This year we will say that a rectangular sheet is "contemporary" if, by cutting it into 2020 equal parts obtained with cuts parallel to its shorter side, one obtains 2020 rectangles that have the same shape as the initial one. If the short side of a contemporary sheet measures 1, how long is the other side?
Pick one
Solution
Solution:
The answer is (A). Let us denote by x the length of the long side of the contemporary sheet. The cut-out rectangles have the same ratio between the sides, but we know that their long side measures 1, while their short side measures 2020x. Writing the equality between the ratios, that is, the proportion, we have: x:1=1:2020x from which x2=2020 that is x=2020
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