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 30 cm by 40 cm. Determine the dimensions of the squares that must be cut out to create the box with a volume of 1872 cm3.

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To determine the dimensions of the squares that must be cut out, we'll have to find the length of one side of the square.

Let's assume that the side length of the square is 'x' cm.

When the squares are cut out and the box is formed, the length and width of the box will be reduced by 2x (since each corner has an x cm square cut out).

So, the length of the box will be 30 - 2x cm, and the width of the box will be 40 - 2x cm.

The height of the box will be equal to the side length of the square, which is x cm.

The volume of the box can be calculated by multiplying the length, width, and height.

Therefore, we have the equation: (30 - 2x) * (40 - 2x) * x = 1872 cm³.

Now, we can solve this equation to find the value of 'x'.

1. Expand the equation: (30 - 2x) * (40 - 2x) * x = 1872
2. Simplify: (1200 - 100x - 60x + 4x²) * x = 1872
3. Combine like terms: (4x² - 160x + 1200) * x = 1872
4. Simplify further: 4x³ - 160x² + 1200x = 1872
5. Subtract 1872 from both sides: 4x³ - 160x² + 1200x - 1872 = 0

At this point, we can either try to solve the cubic equation or use numerical methods to approximate the value of 'x'.

solve (30-2x)(40-2x)x = 1872