Question

An open box is made from a 30cm by 40cm piece of tin by cutting

Answer 1

`\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}`

s represents the square

`\begin{gathered} s_(1,\: 2)=(-\left(-35\right)\pm√(\left(-35\right)^2-4\cdot\:1\cdot\:34))/(2\cdot\:1) \\ s_(1,\: 2)=(-\left(-35\right)\pm\:33)/(2\cdot\:1) \\ s_1=(-\left(-35\right)+33)/(2\cdot\:1)=(35+33)/(2)=(68)/(2)=34 \\ s_2=(-\left(-35\right)-33)/(2\cdot\:1)=(35-33)/(2)=(2)/(2)=1 \end{gathered}`

The length of the sides of the square is 1 cm