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babybri_

  • 3 years ago

If r = 17.2 mm and p = 10.4 mm, which of the following is the range that represents a possible length for q in this triangle? A) 6.8 mm < q < 27.6 mm B) q >= 6.8 mm C) 6.8 mm <= q <= 27.6 mm D)q <= 27.6 mm

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  1. tcarroll010
    • 3 years ago
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    In a triangle, the measure (length) of no one side can be equal to or greater than the sum of the measures of the other 2 sides. So, look for an expression where "q" does not go over a certain value.

  2. babybri_
    • 3 years ago
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    I'm sorry lol I'm a little confused..

  3. jishan
    • 3 years ago
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    c corret

  4. tcarroll010
    • 3 years ago
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    |dw:1355068873536:dw|np, if you have 2 sides that are 5 and 7, then the third side has to be less than 5 + 7 or 12, because you would have something like this otherwise:

  5. tcarroll010
    • 3 years ago
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    And in that case, you would see that the 2 shortest sides could never connect.

  6. babybri_
    • 3 years ago
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    Oooh okay okay I get it

  7. tcarroll010
    • 3 years ago
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    This is one of those "a picture says a thousand words" problems!

  8. babybri_
    • 3 years ago
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    Haha yeah it is!

  9. babybri_
    • 3 years ago
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    Thank's for your help!

  10. tcarroll010
    • 3 years ago
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    You're welcome!

  11. tcarroll010
    • 3 years ago
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    One more thing.

  12. babybri_
    • 3 years ago
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    Yeahh..?

  13. babybri_
    • 3 years ago
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    Like the ones that say <= ?

  14. tcarroll010
    • 3 years ago
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    Actually, I just saw the correct answer. It is indeed listed correctly. But it is a little tricky, so I'll stick around if you want to try it out.

  15. babybri_
    • 3 years ago
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    Yes please!!

  16. tcarroll010
    • 3 years ago
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    Definitely. Here's a hint: that relationship that I described above has to hold for all 3 types. That is: p < q + r q < p + r r < p + q So, that is the trick. All 3 relationships have to be satisfied.

  17. tcarroll010
    • 3 years ago
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    One more hint: 2 of the selections look very similar and it will be the one with the inequalities in it, not the mixed "inequality with equality"

  18. tcarroll010
    • 3 years ago
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    So, back to my example of where you have 2 sides where one is 5 and one is 7. The third side has to be shorter than 12, but it also has to longer than 2 2 < third side < 12 because if it is longer than (or equal to) 12, then it is greater than (or =) 5 + 7 if it is shorter than (or =) 2, then 7 is greater than (or =) 5 + the third side

  19. tcarroll010
    • 3 years ago
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    So, with this information, are you able to get the correct range now?

  20. babybri_
    • 3 years ago
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    Yeah thank you!

  21. tcarroll010
    • 3 years ago
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    You're welcome!

  22. phi
    • 3 years ago
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    one way to see the answer: hook together r = 17.2 mm and p = 10.4 mm with a hinge. if you close them, you get the shortest possible 3rd side if you open them into a line, you get the longest possible 3rd side |dw:1355073170590:dw|

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