Question 120701
Let x = width
2x= length


Now, to get the height, if the length is 1 less than the height, then the height is one more than the length.  So,
2x+1 = height


V=L*W*H
{{{40 = (2x)*x*(2x+1) }}}
{{{2x^2(2x+1)=40 }}}
{{{4x^3 +2x^2 -40=0}}}
{{{2(2x^3+x^2-20) =0}}}


Since this is a cubic equation (that is, {{{x^3 }}} equation), solving it is a fairly advanced topic.  It might be easier to solve {{{2x^3+x^2-20=0}}} by trial and error.


Start by trying x=1.  It doesn't work.

Try x=2:  
{{{2x^3+x^2-20=0}}} 
{{{2*2^3+2^2-20=0}}} 
{{{2*8+4-20=0}}}  This works, so 
x=2 in.  Width
2x= 4 in. Length
2x+1=5 in.  Height


Check:  2*4*5 = 40 cu in.


If you need to solve the cubic equation, you might want to see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com.  Go to "MATH IN LIVING COLOR", look for College Algebra, Section 3.04 Factoring by Synthetic Division.  Graphing calculator methods may also be very helpful in solving such an equation.  Send me an Email if you have additional questions on any of this.


R^2