SOLUTION: This is a factoring word problem when ou have to use the principle of zero. The question is "A box 1 foot tall has a rectangular base with a length that is 1 foot more than the wid

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is a factoring word problem when ou have to use the principle of zero. The question is "A box 1 foot tall has a rectangular base with a length that is 1 foot more than the wid      Log On


   

Question 120196: This is a factoring word problem when ou have to use the principle of zero. The question is "A box 1 foot tall has a rectangular base with a length that is 1 foot more than the width. What are the dimensions of the base if the volume of the box is 6 feet^3?" I don't understand this problem. Could you please help me?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let W=width, L=length


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

L=W%2B1


Now since the volume of any box is

V=L%2AW%2AH

we can plug in the given info


6=%28W%2B1%29%2AW%2A1 Plug in V=6, L=W%2B1, and H=1


6=W%28W%2B1%29 Multiply and rearrange



6=W%5E2%2BW Multiply and rearrange


0=W%5E2%2BW-6 Subtract 6 from both sides



0=%28w%2B3%29%28w-2%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
w%2B3=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%2B1=2%2B1=3 feet