Question 204343
Let L = the length of the finished box and W = is width. If h = its height, then: (The corners are assumed to be square with side = x)
{{{L = 60-2x}}}
{{{W = 40-2x}}} and...
{{{h = x}}}
The surface area, (4 sides plus bottom) SA (as a function of x), can be expressed as:
{{{SA = 2(x(60-2x))+2(x(40-2x))+(60-2x)(40-2x)}}} Simplify.
{{{SA = (2(60x-2x^2))+(2(40x-2x^2))+(2400-200x+4x^2)}}}
{{{SA = 120x-4x^2+80x-4x^2+2400-200x+4x^2}}}
{{{highlight(SA = -4x^2+2400)}}}
For the volume:
{{{V = L*W*h}}}
{{{V = (60-2x)(40-2x)(x)}}}
{{{V = (2400-200x+4x^2)X}}}
{{{highlight_green(V = 4x^3-200x^2+2400x)}}}