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my daughter has a question and I am lost how to solve it.

I have a rectangular box with the following dimensions (see below picture)

Height: $2x-1$

Width: $x+8$

Length: $2x+4$

the line running across the rectangle from bottom left corner to top right corner (sorry don't know name of): $3x+9$

'Setup an equation and solve for $x$' - I don't know how to find $x$ given the above information

I'm pretty sure I could work out the rest of the question once I know what $x$ is

enter image description here

kurasa
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1 Answers1

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First find the diagonal of the top side (using Pythagoras theorem in the triangle formed by the top side's diagonal, length and width):

$(x + 8) ^ 2 + (2x + 4) ^ 2 = D^2$

Then using pythagoras theorem in the triangle formed by the body diagonal, top side's diagonal and the height we get:

$D^2 + (2x - 1) ^ 2 = (3x + 9) ^ 2$

Comparing the 2 above equations we get:

$(x + 8) ^ 2 + (2x + 4) ^ 2 = (3x + 9) ^ 2 - (2x - 1) ^ 2$

Now solve for $x$.

Aneesh Dogra
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  • Maybe I am missing something, but this doesn't make sense to me and gives $x = 0$, which gives a negative length for one of the sides. – Amzoti Mar 17 '13 at 06:08
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    @Amzoti the steps are right. If $x=0$, it is not the answer's fault but the question's. –  Mar 17 '13 at 06:37
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    @amzoti yes the teacher was trying to be 'tricky' - it doesn't make sense and can not be real as the length is negative – kurasa Apr 04 '13 at 01:01