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anonymous

  • one year ago

A right triangle has a 24-cm perimeter, and its hypotenuse is twice as long as it's shortest leg. To the nearest tenth of an inch. find the length of all three sides.

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  1. anonymous
    • one year ago
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    |dw:1441158039904:dw|

  2. anonymous
    • one year ago
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    now we need the third side which we can fine by pythagoras

  3. anonymous
    • one year ago
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    isn't it a 30 60 90 triangle?

  4. anonymous
    • one year ago
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    yes, it is

  5. anonymous
    • one year ago
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    i'm just confused how to find the lengths i wrote out an equation but it's confusing me

  6. anonymous
    • one year ago
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    so the length of the long let is the length of the short leg times \(\sqrt{3}\)

  7. anonymous
    • one year ago
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    |dw:1441158247268:dw|

  8. anonymous
    • one year ago
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    you have \[x+2x+\sqrt{3}x=24\]

  9. anonymous
    • one year ago
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    ok you are ahead of me

  10. anonymous
    • one year ago
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    haha sorry

  11. anonymous
    • one year ago
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    \[3x+\sqrt{3}x=24\] good

  12. anonymous
    • one year ago
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    now the question is, how do you solve for \(x\) right?

  13. anonymous
    • one year ago
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    yeah that's what i'm confused on

  14. anonymous
    • one year ago
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    don't you multiply by one in the form of root three over root three?

  15. anonymous
    • one year ago
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    suppose \(\sqrt{3}=1.7\) and you had \(3x+1.7x=24\) what would you do?

  16. anonymous
    • one year ago
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    4.7x = 24, then you'd divide

  17. anonymous
    • one year ago
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    right and you got \(4.7\) by taking \(3+1.7\) you do the same thing here

  18. anonymous
    • one year ago
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    \[(3+\sqrt{3})x=24\] then divide

  19. anonymous
    • one year ago
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    okay, how would i solve if i needed to keep everything in simple radical form ?

  20. anonymous
    • one year ago
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    does it say round?

  21. anonymous
    • one year ago
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    it does but usually the teacher wants it in the other form

  22. anonymous
    • one year ago
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    http://www.wolframalpha.com/input/?i=24%2F%283%2Bsqrt%283%29%29

  23. anonymous
    • one year ago
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    you can rationalize the denominator if you like

  24. anonymous
    • one year ago
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    okay, i think i get it. thank you

  25. anonymous
    • one year ago
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    yw

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