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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.

  • 8 months ago
  • 8 months ago

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  1. dumbcow
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    use fact the diagonal of a square is sqrt2 times side length |dw:1375640019150:dw|

    • 8 months ago
  2. highschoolmom2010
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    |dw:1375640072724:dw|

    • 8 months ago
  3. highschoolmom2010
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    is that how i need to set it up?

    • 8 months ago
  4. gypsy1274
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    Looks good to me. Do you know where to go from there?

    • 8 months ago
  5. highschoolmom2010
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    eh not really well ....

    • 8 months ago
  6. gypsy1274
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    I would use the pythagorean theorem to find the length of the sides. Does that help?

    • 8 months ago
  7. highschoolmom2010
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    so x^2+x^2=20^2 x^2+x^2=400^@

    • 8 months ago
  8. gypsy1274
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    Before taking the square root, divide both sides by 2.

    • 8 months ago
  9. gypsy1274
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    \(x^2+x^2 = 20^2\) \(2x^2=400\)

    • 8 months ago
  10. dumbcow
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    haha ok i guess you didn't get my drawing...you could just say \[\sqrt{2} x = 20\] \[x = \frac{20}{\sqrt{2}}\]

    • 8 months ago
  11. highschoolmom2010
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    oh ok \[\frac{ 2x^2 }{ 2 }=\frac{ 400 }{ 2 }\] \[x^2=200\] \[\sqrt{x^2}=\sqrt{200}\]

    • 8 months ago
  12. highschoolmom2010
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    |dw:1375640872842:dw| what do i do from here

    • 8 months ago
  13. gypsy1274
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    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.

    • 8 months ago
  14. dumbcow
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    they want answer as decimal so no point in simplifying radical ...

    • 8 months ago
  15. dumbcow
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    haha:)

    • 8 months ago
  16. gypsy1274
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    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.

    • 8 months ago
  17. highschoolmom2010
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    well if i needed the simple radical i was headed right :DD

    • 8 months ago
  18. highschoolmom2010
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    \[\approx 14.14\]

    • 8 months ago
  19. gypsy1274
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    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....

    • 8 months ago
  20. highschoolmom2010
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    \[\approx14\]

    • 8 months ago
  21. highschoolmom2010
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    sorry i forgot that for a second

    • 8 months ago
  22. gypsy1274
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    \(\approx14.1\)

    • 8 months ago
  23. highschoolmom2010
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    oh well i got that all mixed up

    • 8 months ago
  24. gypsy1274
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    You did well.

    • 8 months ago
  25. highschoolmom2010
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    ty @gypsy1274 & @dumbcow

    • 8 months ago
  26. gypsy1274
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    Your welcome.

    • 8 months ago
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