Question 1003752
volume = length * width * height


volume = 252


length * width * height = 252


your height will be 4 cm because you are cutting our 4 cm squares from each end and then folding up what is left.


your width is assumed to be x.


if your width is x, then your length has to be x + 2.


length * width * height = 252 becomes:


(x + 2) * x * 4 = 252


divide both sides of this equation by 4 to get:


(x + 2) * x = 63


simplify to get:


x^2 + 2x = 63


subtract 63 from both sides of this equation to get:


x^2 + 2x - 63 = 0


factor this quadratic equation to get:


(x + 9) * (x - 7) = 0


solve for x to get:


x = -9 or x = 7


x can't be negative, so you are left with x = 7


that's the width.


the length is equal to 2 + 2 which is equal to 9.


your box will have dimensions of:


length = 9
width = 7
height = 4


now you have to figure out what size paper you will need.


the length of your paper will have to be 9 cm + 4 cm on each end = 9 cm + 8 cm = 17 cm.


the width of your paper will have to be 7 cm + 4 cm on each end = 7 cm + 8 cm = 15 cm.


your paper will have to be 17 cm by 15 cm.


a picture of what your paper will look like after you marked it for cutting is shown below:


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