Marinada '24

[lang=hr] Zadan je kvadrat sa stranicom duljine $37$. Nad jednom stranicom tog kvadrata konstruiran je pravokutni trokut kojem je hipotenuza stranica tog kvadrata i jedna kateta duljine $12$. Nad duljom katetom pravokutnog trokuta konstruiran je kvadrat tako da mu je jedna stranica ta kateta pa je ponovno konstruiran pravokutni trokut, koji je sličan onome iz prethodnog koraka. Ako nastavimo ovaj postupak, izračunaj duljinu stranice tako konstruiranog $24.$ kvadrata. Napomena: na početku zadan kvadrat je prvi kvadrat od $24$. [/lang] [lang=en] A square with a side length of $37$ is given. On one side of the square, a right triangle is constructed where the hypotenuse is that side of the square, and one leg has a length of $12$. On the longer leg of this right triangle, another square is constructed such that one side of the square is that leg, and then another right triangle is constructed, similar to the one in the last step. If this process continues, calculate the side length of the $24^{\text{th}}$ square constructed in this manner. Note: The initially given square is the first of the $24$. [/lang]