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highschoolmom2010

  • 2 years ago

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

  2. highschoolmom2010
    • 2 years ago
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    |dw:1375640072724:dw|

  3. highschoolmom2010
    • 2 years ago
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    is that how i need to set it up?

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

  5. highschoolmom2010
    • 2 years ago
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    eh not really well ....

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

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

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

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

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

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

  12. highschoolmom2010
    • 2 years ago
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    |dw:1375640872842:dw| what do i do from here

  13. gypsy1274
    • 2 years ago
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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.

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

  15. dumbcow
    • 2 years ago
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    haha:)

  16. gypsy1274
    • 2 years ago
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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.

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

  18. highschoolmom2010
    • 2 years ago
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    \[\approx 14.14\]

  19. gypsy1274
    • 2 years ago
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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....

  20. highschoolmom2010
    • 2 years ago
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    \[\approx14\]

  21. highschoolmom2010
    • 2 years ago
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    sorry i forgot that for a second

  22. gypsy1274
    • 2 years ago
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    \(\approx14.1\)

  23. highschoolmom2010
    • 2 years ago
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    oh well i got that all mixed up

  24. gypsy1274
    • 2 years ago
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    You did well.

  25. highschoolmom2010
    • 2 years ago
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    ty @gypsy1274 & @dumbcow

  26. gypsy1274
    • 2 years ago
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    Your welcome.

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