Question 964452
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The area of the bottom of the box is given by:
{{{765cm^3/3cm=255cm^2}}}
The length of the box is still 2 cm longer than the width.
{{{W[b]=box width}}}; {{{L[b]=box length}}}={{{W[b]+2cm}}}; {{{A[b]=box area}}}
{{{A[b]=L[b]W[b]}}} Substitute for {{{L[b]}}}
{{{255cm^2=(W[b]+2cm)(W[b])}}}Subtract 255cm^2 from each side.
{{{0=W[b]^2+2W[b]-255}}}
{{{0=(W[b]+17)(W[b]-15)}}}
{{{W[b]+17=0}}} {{{or}}} {{{W[b]-15=0}}}
{{{W[b]=-17}}} {{{or}}} {{{W[b]=15}}}
Width of the box is 15cm
Length of box=width+2cm=17cm
The original cardboard is 6cm longer (3cm folded up on each end)
and 6cm wider (3cm folded up on each side)so:
{{{L[b]+6cm=17cm+6cm}}}={{{23cm}}} ANSWER 1: The cardboard rectangle was 23 cm long.  
{{{W[b]+6cm=15cm+6cm}}}={{{21cm}}} ANSWER 2: The cardboard rectangle was 21 cm wide.