Question

Surface area of a rectangular box, with height of 17-2x, width of 12-2x, and height of x.

We're trying 2(12-2x)(17-2x)+2(x)(12-2x)+2(x)(17-2x), but it says that is not right

Answer 1

The correct expression for the surface area of the rectangular box is
`\( A = -72x + 408 \).`

The formula for the surface area A of a rectangular box is given by:

`\[ A = 2lw + 2lh + 2wh \]`

where I, w, and h are the length, width, and height of the box, respectively.

In this case, you have stated that the height is
`\(17-2x\)`, the width is
`\(12-2x\),` and the length is x. So, the correct expression for the surface area should be:

`\[ A = 2(x)(12-2x) + 2(x)(17-2x) + 2(12-2x)(17-2x) \]`

Now, let's expand and simplify this expression:

`\[ A = 2x(12-2x) + 2x(17-2x) + 2(12-2x)(17-2x) \]\\A = 24x - 4x^2 + 34x - 4x^2 + 2(12-2x)(17-2x) \]\\A = 58x - 8x^2 + 2(12-2x)(17-2x) \]`

Now, distribute and simplify the remaining terms:

`\[ A = 58x - 8x^2 + 2(204 - 68x - 24x + 4x^2) \]\\ A = 58x - 8x^2 + 408 - 136x - 48x + 8x^2 \]`

Combine like terms:

`\[ A = -72x + 408 \]`

So, the correct expression for the surface area of the rectangular box is
`\( A = -72x + 408 \).`