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Formulating Mathematical Statements.

Given Statements

• Length is 12 cm longer than the width
• A open box is to be formed out.
• A square of side 5 cm will be removed from each corner of the cardboard.
• The box is to hold at most 1900 cm³

We can assume that the open box is a rectangular cube. The volume of the cube would be.

V = LWH

• where L is the length
• where W is the width
• where H is the height

Formulating the statements of the given dimensions.

Length would be x + 12

Width would be x

Height is the length of the cutted corner, so it would be 5

Since we have to also cut out the sides of the boxes by 5 cm, we would have to reduce the dimensions of length and width. In a quadrilateral there would be 4 edges, so it would be reduced by double per dimension except for the height.

So in conclusion

Length would be x + 12 - 10, so the new length is x + 2

Width would be x - 10

Then substitute the values in the formula. One more thing, the question that it must be at most 1900 cm³ so it would be an inequality.

LWH ≤ A

(x + 2)(x - 10)(5) ≤ 1900

(x² - 10x - 2x - 20)(x) ≤ 1900

(x² - 8x - 20)(5) ≤ 1900

5x² - 40x - 100 ≤ 1900

The mathematical statement is

5x² - 40x - 100x ≤ 1900

I hope it helps and my answer is correct ^-^

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