[tex]\begin{gathered} (30-2s)\cdot(40-2s)=1064 \\ 1200-60s-80s+4s^2=1064 \\ 4s^2-140s+1200=1064 \\ 4s^2-140s+136=0 \\ s^2-35s+34=0 \end{gathered}[/tex]
s represents the square
[tex]\begin{gathered} s_{1,\: 2}=\frac{-\left(-35\right)\pm\sqrt{\left(-35\right)^2-4\cdot\:1\cdot\:34}}{2\cdot\:1} \\ s_{1,\: 2}=\frac{-\left(-35\right)\pm\:33}{2\cdot\:1} \\ s_1=\frac{-\left(-35\right)+33}{2\cdot\:1}=\frac{35+33}{2}=\frac{68}{2}=34 \\ s_2=\frac{-\left(-35\right)-33}{2\cdot\:1}=\frac{35-33}{2}=\frac{2}{2}=1 \end{gathered}[/tex]
The length of the sides of the square is 1 cm
