Question #ec7ee

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Question #ec7ee

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Answer 1 · 2017-03-08T07:21:28

The dimensions are $12 x by 8 x by 4 x$ $12x " by " 8x " by " 4x$ 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. $4 + 4 + 4 = 12$ $4+4+4 = 12$ inches

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

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

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

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

The dimensions of the box are therefore:

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

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:

$V = l \times b \times h = 12 x \times 8 x \times 4 x = 384 x^{3}$ $V = lxxbxxh = 12x xx 8x xx 4x = 384x^3$

If it is the total surface area it would be:

$T S A = 2 (l b + l h + b h) = 2 (12 x \times 8 x + 12 x \times 4 x + 8 x \times 4 x)$ $TSA = 2(lb+lh +bh) = 2(12x xx 8x + 12x xx 4x +8x xx 4x)$

$= 2 (96 x^{2} + 48 x^{2} + 32 x^{2})$ $=2(96x^2 +48x^2 +32x^2)$

$= 2 (176 x^{2}) = 352 x^{2}$ $=2(176x^2) = 352x^2$

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Question #ec7ee

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