highschoolmom2010
  • highschoolmom2010
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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SOLVED
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katieb
  • katieb
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dumbcow
  • dumbcow
use fact the diagonal of a square is sqrt2 times side length |dw:1375640019150:dw|
highschoolmom2010
  • highschoolmom2010
|dw:1375640072724:dw|
highschoolmom2010
  • highschoolmom2010
is that how i need to set it up?

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More answers

anonymous
  • anonymous
Looks good to me. Do you know where to go from there?
highschoolmom2010
  • highschoolmom2010
eh not really well ....
anonymous
  • anonymous
I would use the pythagorean theorem to find the length of the sides. Does that help?
highschoolmom2010
  • highschoolmom2010
so x^2+x^2=20^2 x^2+x^2=400^@
anonymous
  • anonymous
Before taking the square root, divide both sides by 2.
anonymous
  • anonymous
\(x^2+x^2 = 20^2\) \(2x^2=400\)
dumbcow
  • dumbcow
haha ok i guess you didn't get my drawing...you could just say \[\sqrt{2} x = 20\] \[x = \frac{20}{\sqrt{2}}\]
highschoolmom2010
  • highschoolmom2010
oh ok \[\frac{ 2x^2 }{ 2 }=\frac{ 400 }{ 2 }\] \[x^2=200\] \[\sqrt{x^2}=\sqrt{200}\]
highschoolmom2010
  • highschoolmom2010
|dw:1375640872842:dw| what do i do from here
anonymous
  • anonymous
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.
dumbcow
  • dumbcow
they want answer as decimal so no point in simplifying radical ...
dumbcow
  • dumbcow
haha:)
anonymous
  • anonymous
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.
highschoolmom2010
  • highschoolmom2010
well if i needed the simple radical i was headed right :DD
highschoolmom2010
  • highschoolmom2010
\[\approx 14.14\]
anonymous
  • anonymous
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....
highschoolmom2010
  • highschoolmom2010
\[\approx14\]
highschoolmom2010
  • highschoolmom2010
sorry i forgot that for a second
anonymous
  • anonymous
\(\approx14.1\)
highschoolmom2010
  • highschoolmom2010
oh well i got that all mixed up
anonymous
  • anonymous
You did well.
highschoolmom2010
  • highschoolmom2010
ty @gypsy1274 & @dumbcow
anonymous
  • anonymous
Your welcome.

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