What is the side length of the smallest square plate on which a 20-cm chopstick can fit along a diagonal without any overhang? Round your answer to the nearest tenth of a centimeter.

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What is the side length of the smallest square plate on which a 20-cm chopstick can fit along a diagonal without any overhang? Round your answer to the nearest tenth of a centimeter.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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use fact the diagonal of a square is sqrt2 times side length |dw:1375640019150:dw|
|dw:1375640072724:dw|
is that how i need to set it up?

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Looks good to me. Do you know where to go from there?
eh not really well ....
I would use the pythagorean theorem to find the length of the sides. Does that help?
so x^2+x^2=20^2 x^2+x^2=400^@
Before taking the square root, divide both sides by 2.
\(x^2+x^2 = 20^2\) \(2x^2=400\)
haha ok i guess you didn't get my drawing...you could just say \[\sqrt{2} x = 20\] \[x = \frac{20}{\sqrt{2}}\]
oh ok \[\frac{ 2x^2 }{ 2 }=\frac{ 400 }{ 2 }\] \[x^2=200\] \[\sqrt{x^2}=\sqrt{200}\]
|dw:1375640872842:dw| what do i do from here
Yes, that would be great if you were supposed to have a radical in your answer, but your question says to round to the nearest tenth, so use a calculator (or google) to get the square root of 200.
they want answer as decimal so no point in simplifying radical ...
haha:)
You might want to save @dumbcow's original picture and equation to spend a rainy day in contemplation. If you can remember it the next time you need it, that would be a quicker way of getting to the answer.
well if i needed the simple radical i was headed right :DD
\[\approx 14.14\]
Yes, you simplified the radical very well. And in later classes, you will probably need to leave your answer like that. Rounded to the nearest tenth is one place after the decimal....
\[\approx14\]
sorry i forgot that for a second
\(\approx14.1\)
oh well i got that all mixed up
You did well.
Your welcome.

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