Question

A machine produces open boxes using square sheets of metal. The machine cuts​ equal-sized squares measuring 2

inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 50

cubic​ inches, find the length and width of the open box.

Answer 1

check the picture below

thus


`\bf 50=2x^2-16x+32\implies 25=x^2-8x+16 \\\\\\ 0=x^2-8x-9\implies 0=(x-9)(x+1)\implies x= \begin{cases} \boxed{9}\\ -1 \end{cases}`

it cannot be a negative value, so can't be -1