1. If an A4 sheet is precisely cut in half along a straight line parallel to the shorter side, two sheets are created that have the same shape as the original, i.e., they are obtained from it through a rotation and a reduction in scale. 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, 2020 rectangles are obtained that have the same shape as the initial one. If the shorter side of a contemporary sheet measures 1, how long is the other side?
(A) $\sqrt{2020}$
(B) $2020^{3 / 2}$
(C) $\frac{2021}{2}$
(D) 2020
(E) None of the above
1. The answer is $\mathbf{( A )}$. Let $x$ be the length of the longer side of the contemporary sheet. The rectangles that are cut out have the same ratio between their sides, but we know that their longer side measures 1, while their shorter side measures $\frac{x}{2020}$. Writing the equality between the ratios, that is, the proportion, we have: $x: 1=1: \frac{x}{2020}$, from which $x^{2}=2020$, that is $x=\sqrt{2020}$.