An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with a volume of 1008cm^3.

length=30-2x
width=20-2x
h=x
I don't get this because x and cm aren't interchangeable digits.

no idea what your complaint is about. x is a variable, and its units are cm. Multiply the three expressions and you get cm^3.

x(20-2x)(30-2x) = 1008
4x^3 - 100x^2 + 600x - 1008 = 0
scale down by 4:
x^3 - 25x^2 + 150x - 252 = 0

252 = 2*2*3*3*7
The only integer root is x=3, so the required box is

3×14×24 = 1008

Why is it always (whatever number -2x)? why the -2x?

Well, isn't that a dilemma, trying to mix up letters and numbers like that? It's like trying to put a square peg in a round hole. Or in this case, trying to interchange x and cm. You see, x represents the length of the squares to be cut, whereas cm represents centimeters, a unit of measurement. So, my funny friend, to solve this confusion, let's stick to using x to represent the length of the squares that need to be cut and cm to represent centimeters, the unit of measurement. Deal? Deal.

Now, back to the problem. The volume of the box can be found by multiplying its length, width, and height. In this case, the length and width of the box are given by (30 - 2x) cm and (20 - 2x) cm, respectively, and the height is simply x cm. We are told that the volume of the box is 1008 cm^3. So, we can set up the equation:

(30 - 2x)(20 - 2x)(x) = 1008

Now, solving this equation may require some mathematical prowess that I'm not too fond of, but I'll leave that up to you. Just remember, math is like a puzzle - sometimes you have to think outside the box to find the right solution. Good luck!

I understand your confusion. In this case, "x" is being used as a variable to represent the length of the sides of the squares that are being cut from the corners of the cardboard. The dimensions of the box itself are expressed in centimeters because we are dealing with physical measurements.

To solve this problem step-by-step, we need to use the given information and equations related to volume. Here's how we can approach it:

1. Start with the given dimensions of the cardboard: length = 30 cm and width = 20 cm.
2. Cut congruent squares with side length "x" from each of the four corners.
3. After cutting the squares and folding up the sides, the length and width of the resulting box will be reduced by "2x" (the length of each cut square is deducted twice).
4. Therefore, the length of the box will be (30 - 2x) cm and the width will be (20 - 2x) cm.
5. The height of the box will be equal to the side length of the cut square, which is "x" cm.
6. The volume of the box can be calculated by multiplying the length, width, and height: volume = (30 - 2x)(20 - 2x)(x).
7. We are given that the volume of the box is 1008 cu.cm, so we can set up the equation: (30 - 2x)(20 - 2x)(x) = 1008.
8. Now, we need to solve this equation to find the value of "x" by simplifying and factoring.
9. Once we find the value of "x," we can substitute it back into the expressions for length, width, and height to determine the dimensions of the squares that must be cut to create the desired box.

By following these steps, we can determine the dimensions of the squares that need to be cut from the corners of the cardboard to create a box with a volume of 1008 cm^3.

Actual length = 23•8m 1cm to 2m