SOLUTION: The area of a rectangular piece of cardboard is 1008cm^2. If you cut a 4 cm square from each corner of the rectangular piece of cardboard and turn up the sides then an open box is

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The area of a rectangular piece of cardboard is 1008cm^2. If you cut a 4 cm square from each corner of the rectangular piece of cardboard and turn up the sides then an open box is       Log On


   

Question 1056003: The area of a rectangular piece of cardboard is 1008cm^2. If you cut a 4 cm square from each corner of the rectangular piece of cardboard and turn up the sides then an open box is formed whose volume is 2240cm^3. Find the dimensions of the rectangular piece of cardboard and the dimensions of the open box.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x and y are the uncut, unfolded cardboard dimensions.

Cutting out the square shaped corners of 4cm sides and folding produces a base area of (x-2*4) and (y-2*4) and this base area is %28x-8%29%28y-8%29. You are given in description that xy=1008.

Also is given the volume of the resulting rectangular box, of last dimension 4.

Volume is 4%28x-8%29%28y-8%29=2240.

Solve this system for x and y.
system%284%28x-8%29%28y-8%29=2240%2Cxy=1008%29
which is equivalent to more simplified system of
system%28%28x-8%29%28y-8%29=560%2Cxy=1008%29.
If you are able to handle the algebra steps from here, then you can finish.