Question 701738

The volume of a box is {{{V=L*W*h}}} where {{{L=length}}}, {{{W=width}}} and {{{h=height}}}

given:
the volume of a box is {{{V=1755ft^3}}}
the width of the box is {{{highlight(W=9ft)}}}, 

and it's height {{{h}}} is {{{2ft}}} more than it's length {{{L}}}; so, {{{h=L+2}}}


to find: the height of the box {{{h}}}

start with {{{V=L*W*h}}}...plug in given values


{{{1755=a*9*(a+2)}}}

{{{1755=9ft*(a^2+2a)}}}

{{{1755=9a^2+18a}}}

{{{0=9a^2+18a-1755}}}.......use quadratic formula


{{{L = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{L = (-18+- sqrt( 18^2-4*9*(-1755 )))/(2*9) }}}


{{{L = (-18+- sqrt( 324+63180))/18 }}}


{{{L = (-18+- sqrt( 63504))/18 }}}


{{{L = (-18+- 252)/18 }}}


{{{L = (-18+ 252)/18 }}}..we will find only positive solution because the length could be only positive number

{{{L = (-18+ 252)/18 }}}


{{{L = 234/18}}}
 

{{{highlight(L = 13ft)}}}

now we can find the height {{{h}}}

{{{h=L+2ft}}}

{{{h=13ft+2ft}}}

{{{highlight(h=15ft)}}}