#### greentree.23

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- Thread starter greentree.23
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What i’ve done so far is:

Let width = x = AB = DC = GH = FE

Let length = y = EH = AD = BC = FG

Let height = z = AE = DH =BF = CG.

AH^2 = 6^2 = z^2 + y^2 using Pythag.

AG^2 = ?

AC^2 = x^2 + y^2

AF^2 = 4^2 = ?

And I’m stuck from here

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You should have three equations, for AC, AF, and AH. I don't know why you didn't finish AF and AC.What i’ve done so far is:

Let width = x = AB = DC = GH = FE

Let length = y = EH = AD = BC = FG

Let height = z = AE = DH =BF = CG.

AH^2 = 6^2 = z^2 + y^2 using Pythag.

AG^2 = ?

AC^2 = x^2 + y^2

AF^2 = 4^2 = ?

And I’m stuck from here

Then, to write an equation for AG, observe that ACG is a right triangle.

Then start putting things together.

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You should have three equations, for AC, AF, and AH. I don't know why you didn't finish AF and AC.

Then, to write an equation for AG, observe that ACG is a right triangle.

Then start putting things together.

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Having defined your variables, why didn't you use them?What i’ve done so far is:

Let width = x = AB = DC = GH = FE

Let length = y = EH = AD = BC = FG

Let height = z = AE = DH =BF = CG.

AH^2 = 6^2 = z^2 + y^2 using Pythag.

AG^2 = ?

AC^2 = x^2 + y^2

AF^2 = 4^2 = ?

And I’m stuck from here

based on this diagram...

you could have said....

x² + y² = 3² \(\displaystyle \implies\) **x² + y² = 9**

x² + z² = 4² \(\displaystyle \implies\) **x² + z² = 16**

y² + z² = 6² \(\displaystyle \implies\) **y² + z² = 36**

Let us call AG

But let us now also call AC "

Therefore,

It is possible to manipulate the three equations above to arrive at an

Notwithstanding that fact, all you are asked to do is arrive at a "value" for

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I'm not too sure on how to manipulate the other equations to solve side AG using Pythagoras. 3^2 + z^2 = AG^2 and I'm stuck from here?This doesn't seem to be possible.

I will not show my work as I want the OP to solve this problem.

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ItThis doesn't seem to be possible.

I will not show my work as I want the OP to solve this problem.

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Can you give a hint on how to solve it algebraically?Itpossible to solve it algebraically (body diagonal of a cuboid) but the prism just can'tiswith those dimensions.exist

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You lost me. If the prism can't exist, then how can you find the diagonal of the prism, you know, the one that doesn't exist??Itpossible to solve it algebraically (body diagonal of a cuboid) but the prism just can'tiswith those dimensions.exist

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I can't tell you that for four days or stapel will delete me!You lost me. If the prism can't exist, then how can you find the diagonal of the prism, you know, the one that doesn't exist??

However, (as suggested above) add the equations & simplify.

(I presume that (like me) you found x

* See Post #6.

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[math]2x^2 = -11 = (x^2+y^2) + (x^2 + y^2) - (y^2+z^2) = 9+16-36[/math]

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I didn't know that stapel had the ability to delete people. I'm glad that I've been nice to her.I can't tell you that for four days or stapel will delete me!

but using the formula for the body diagonal of a cuboid*produce a value for the length of AG despite the impossibility of a prism with the given dimensions. )does

How can you find the length of AG, A and G being points in a rectangular prism, if the rectangular prism doesn't exist?

I'm not saying that you're wrong but am saying that I don't understand how you can be correct.

Sometimes I am completely confused with math and other times I just simply love math.

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It exists, but it isn't realHow can you find the length of AG, A and G being points in a rectangular prism, if the rectangular prism doesn't exist?

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I won't blame/hate you, but I am not a fan of math today. It exists, but it isn't realIt exists, but it isn't real

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I have long found it interesting that there are some problems like this for which there is a shortcut to the solution that bypasses work that shows whether there is in fact a solution at all, and just finds the solution -- even when it does not really exist. Unfortunately, I have never made a list of such problems, so I can never point to one.How can you find the length of AG, A and G being points in a rectangular prism, if the rectangular prism doesn't exist?

I'm not saying that you're wrong but am saying that I don't understand how you can be correct.

Sometimes I am completely confused with math and other times I just simply love math.

In this case, we can just add the three equations [math]x^2+y^2=9\\x^2+z^2=16\\y^2+z^2=36[/math] together, and divide by 2, to get [math]x^2+y^2+z^2=30.5[/math] which provides an answer, but since we never actually solved for the individual variables, we don't realize (at least, I did not) that all we've proved is that

Sometimes existence has to be proved separately!