<PRE><B>Question 864024</B>
x side of base
y height
120 square cm, amount of surface to make the box.


Surface area, {{{4*xy+x^2=120}}}.
Volume, {{{v=yx^2}}}.


(a):
To get v=100 cubic cms, try solving surface area equation for y and substitute into the volume equation.
S.A., {{{4xy=120-x^2}}}
{{{y=(120-x^2)/(4x)}}}
-
{{{yx^2=100}}}
{{{((120-x^2)/(4x))x^2=100}}}
{{{(120-x^2)x/4=100}}}
{{{(120-x^2)x=400}}}
{{{-x^3+120x-400=0}}}
{{{highlight(x^3-120x+400=0)}}}
This gives x at 8.6 and 3.75, and you could check each of these for what happens to y using {{{y=(120-x^2)/(4x)}}}.  Graphing tool was used, and not polynomial property skills.</PRE>