SOLUTION: An open box is formed from a rectangular piece of cardboard by cutting 2 cm by 2 cm squares from each corner and then folding up the sides and soldering the seams. The length of th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: An open box is formed from a rectangular piece of cardboard by cutting 2 cm by 2 cm squares from each corner and then folding up the sides and soldering the seams. The length of th      Log On


   

Question 301466: An open box is formed from a rectangular piece of cardboard by cutting 2 cm by 2 cm squares from each corner and then folding up the sides and soldering the seams. The length of the original piece of cardboard was 8 cm more than it's width. If the volume of the open box is +256+cm%5E3, what are the dimensions of the metal box?
Use a polynomial equation.
Also, If you could reply with the initial equation, that would help me understand it better.
P.S. If you can not answer this direct it to the Word Problems: Misc Word Problems tutor.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
L=(W+8-4)
W=W-4
V=LWH
256=(W+8-4)(W-4)2
256=(W+4)(W-4)*2
256=(W^2-16)2
256=2W^2-32
2W^2=32+256
2W^2=288
W^2=288/2
W^2=144
W=SQRT144
W=12 cm. ANS. FOR THE ORIGINAL WIDTH.
L=12+8=20 cm. ANS. FOR THE ORIGINAL LENGTH.
BASE=W-4=12-4=8 cm NEW WIDTH.
BASE=L-4=20-4=16 cm NEW LENGTH.
PROOF:
256=(12+8-4)(12-4)2
256=16*8*2
256=256
256=256