Lorene plans to make several open topped boxes in which to carry plants. she makes the boxes from rectangular sheets of cardboard from which she cuts out 6in squares from each corner. The length of the original piece of cardboard is 12 in more than the width. If the volume of the box is 1950 in squared , determine the dimensions of the original piece of cardboard.

Length = 37 in, Width = 25 in

Step-by-step explanation:

The length of the original cardboard is 12 more than the width, so:

Length = Width + 12

The base of the box will be formed the length minus two cuts of 6in and the width minus two cuts of 6in, so:

Base Area = (Length-12)*(Width-12)

The height of the box will be the 6 inches, after folding the pieces of the cardboard to form a box.

To, if the volume of the box is 1950, we have that:

1950 = Base area * height = (Length-12)*(Width-12)*6

Base Area = 1950/6 = 325

Now, using the length value (Length = Width + 12) in the base area equation, we have:

325 = (Width+12-12)*(Width-12)

325 = Width^2 - 12*Width

Width^2 - 12*Width - 325 = 0

Solving this quadratic equation, we have that:

Delta = b^2 - 4ac = 144 + 1300 = 1444

sqrt(Delta) = 38

Width = (12 + 38)/2 = 25 in

Now, finding the length:

Length = Width + 12 = 25 + 12 = 37 in

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