Question 120196
Let W=width, L=length



Since the "length that is 1 foot more than the width" this means 


{{{L=W+1}}}



Now since the volume of any box is 


{{{V=L*W*H}}}


we can plug in the given info



{{{6=(W+1)*W*1}}} Plug in {{{V=6}}}, {{{L=W+1}}}, and {{{H=1}}}



{{{6=W(W+1)}}} Multiply and rearrange




{{{6=W^2+W}}} Multiply and rearrange



{{{0=W^2+W-6}}} Subtract 6 from both sides




{{{0=(w+3)(w-2)}}} Factor the right side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{w+3=0}}} or  {{{w-2=0}}} 


{{{w=-3}}} or  {{{w=2}}}    Now solve for w in each case



So our answer is 

 {{{w=-3}}} or  {{{w=2}}} 



However, since a negative length doesn't make sense, our only solution is {{{w=2}}}




So the width is 2 feet and the length is {{{W+1=2+1=3}}} feet