Question

Question #ec7ee

Answer 1

The dimensions are `12x " by " 8x " by " 4x` inches.

Explanation:

Let's look at the actual dimensions of the carton first.

The length of the carton will be the width of three dictionaries placed side by side. `4+4+4 = 12` inches

The width of the carton will be the length of one book: `8` inches

The height will be the thickness of four books on top of each other:
`1+1+1+1 = 4` inches

So the carton is `12 " by " 8 " by " 4` inches.

As a polynomial we have to write the dimensions of each book in terms of `x`.
Let's call the thickness `x`
The width of each book is therefore `4x`
and the length is `8x`

The dimensions of the box are therefore:

Length: `4x+4x+4x = 12x`
Width: `8x`
Height: `x+x+x+x=4x`

We can only write a single polynomial if we know what we are doing with the separate dimensions.

If it is the volume of the carton, it would be:

`V = lxxbxxh = 12x xx 8x xx 4x = 384x^3`

If it is the total surface area it would be:

`TSA = 2(lb+lh +bh) = 2(12x xx 8x + 12x xx 4x +8x xx 4x)`

`=2(96x^2 +48x^2 +32x^2)`

`=2(176x^2) = 352x^2`