Question 582525
Let {{{ h }}} = height of box
given:
width = {{{ h - 1 }}}
length = {{{ h + 3 }}}
Volume = width x length x height
{{{ 6 = h*( h - 1 )*( h + 3 ) }}}
{{{ 6 = h*( h^2 - h + 3h - 3 ) }}}
{{{ 6 = h*( h^2 + 2h - 3 ) }}}
{{{ 6 = h^3 + 2h^2 - 3h }}}
{{{ h^3 + 2h^2 - 3h - 6 = 0 }}}
The only way I know to solve this
is to carefully plot it ( or use a program )
Here's the plot:
{{{ graph( 400, 400, -4, 4, -10, 10, x^3 + 2x^2 - 3x - 6 ) }}}
It looks like {{{ h = 1.8 }}} approximately
Then the width is
{{{ h - 1 = .8 }}}
The length is
{{{ h + 3 = 4.8 }}}
The volume would be
{{{ 1.8*.8*4.8 = 6.912 }}} (too much)
-----------
If I say {{{ h = 1.75 }}}
width = {{{ .75 }}}
length = {{{ 4.75 }}}
{{{ 1.75*.75*4.75 = 6.23 }}}
-----------
I'm guessing that {{{ h = 1.7 }}}
The dimensions are
1.7 x .7 x 4.7
( very close )