Answer:
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
