In the square shown in the figure, find the value of $x$.
Problem
Source:
Tags: geometry, square
eagles2018
17.09.2021 00:15
Draw the diagonal from the bottom left to the top right of the square. This is also the diagonal of a $7 \times 23$ rectangle. Thus, the diagonal length is $\sqrt{7^2+23^2}=\sqrt{578}=17\sqrt{2}$. Thus $x\sqrt2=17\sqrt2 \Rightarrow x=17$.
Edit: 1500 post!
jasperE3
17.09.2021 00:16
Does Puerto Rico have a separate team selection process from the US?
parmenides51
17.09.2021 00:20
This is the official Puerto Rico page. They participate separately of USA in IMO, as you may see here
eagles2018
17.09.2021 00:32
Wait, how was this a TST problem? Did I really just solve a TST problem?!!! I did get it correct, right?
Math_Is_Fun_101
17.09.2021 03:12
eagles2018 wrote: Wait, how was this a TST problem? Did I really just solve a TST problem?!!! I did get it correct, right? It looks right! Granted, the Puerto Rico TST isn't as strong as other countries like USA, but still, you solved a TST problem. Nice!