Question

Can someone teach me how to do this? no files or links please

Answer 1

Check the picture below.

we know the box has a square base, meaning the Length = Width, we also know its volume is 400 times its height.

$\textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=h+12\\ w=h+12\\ V=400h \end{cases}\implies 400h=(h+12)(h+12) \\\\\\ 400h=\stackrel{F~O~I~L}{h^2+24h+144}\implies 0=h^2+24h-256 \\\\\\ 0=(h-8)(h+32)\implies h= \begin{cases} 8~~\checkmark\\ -32 \end{cases}$

now, notice, -32 is a valid value for "h", however, the height cannot be a negative value, so we toss that root/solution.

$\stackrel{height}{8}\qquad \qquad \underset{8~~ + ~~12}{\stackrel{length}{20}}\qquad \qquad \underset{8~~ + ~~12}{\stackrel{width}{20}}$