Question 644775
Let the width of the piece of cardboard = {{{ w }}} in
The length = {{{ w + 12 }}} in
After the 4 in squares are cut from each corner,
The width = {{{ w - 8 }}} in
The length = {{{ w + 12 - 8 }}} in
Folding the sides up makes the height {{{ 4 }}} in
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The volume is length x width x height, so
{{{ 256 = ( w - 8 )*( w + 4 )*4 }}} in3
{{{ 256 = ( w^2 - 8w + 4w - 32 )*4 }}}
{{{ 64 = w^2 - 4w - 32  }}}
{{{ w^2 - 4w = 96 }}}
Complete the square
{{{ w^2 - 4w + (4/2)^2 = 96 + (4/2)^2 }}}
{{{ w^2 - 4w + 4 = 100 }}}
{{{ ( w - 2 )^2 = 10^2 }}}
{{{ w - 2 = 10 }}}
{{{ w = 12 }}} in
and length = {{{ 12 + 12 = 24 }}} in
The cardboard is 12" x 24"
Height is 4"
Width is 12"
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check:
The volume is
{{{ V = ( w - 8 )*( w + 4 )*4 }}}
{{{ V = ( 12 - 8 )*( 12 + 4 )*4 }}}
{{{ V = 4*16*4 }}}
{{{ V = 16*16 }}}
{{{ V = 256 }}} in3
OK