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abm1995

  • 3 years ago

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter.

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  1. ash2326
    • 3 years ago
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    Do you have a figure?

  2. abm1995
    • 3 years ago
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    there's no figure. /: sorry.

  3. ash2326
    • 3 years ago
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    No worries, that's why it has asked for two answers. Let ABC be the triangle and AD be the angle bisector. Let BD=6 and DC=5 |dw:1359393342358:dw| Do you understand the figure?

  4. abm1995
    • 3 years ago
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    yes!

  5. ash2326
    • 3 years ago
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    @abm1995 ??

  6. abm1995
    • 3 years ago
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    do you want the choices?

  7. abm1995
    • 3 years ago
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    a. 41.4 cm, 8.3 cm b. 30 cm, 5.8 cm c. 41.4 cm, 4.3 cm d. 8.3 cm, 5.8 cm

  8. abm1995
    • 3 years ago
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    does anyone understand this?

  9. ash2326
    • 3 years ago
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    Now we can have either AB or AC as 6.9 cm, we don't know that. It's the second side. Do you know Angle Bisector theorem?

  10. abm1995
    • 3 years ago
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    no i don't./: i'm dumb.

  11. abm1995
    • 3 years ago
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    do you know the answer? then when i figure it out you will say if i'm right or not?

  12. ash2326
    • 3 years ago
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    Yeah, I'll do let me explain you angle bisector theorem

  13. abm1995
    • 3 years ago
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    ok.

  14. ash2326
    • 3 years ago
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    Angle bisector divides the side opposite to the angle in the same ratio as that of the other two sides of the triangle, for example here|dw:1359394184684:dw| \[\frac{BD}{DC}=\frac {AB}{AC}\]

  15. abm1995
    • 3 years ago
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    oh ok.

  16. abm1995
    • 3 years ago
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    wouldn't the answer be B then?

  17. ash2326
    • 3 years ago
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    here we have BD=6 DC=5 Now assume AB as 6.9, find AC ???

  18. abm1995
    • 3 years ago
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    so b?

  19. ash2326
    • 3 years ago
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    No not yet. We have to find one more thing, assume AC=6.9 and find AB

  20. abm1995
    • 3 years ago
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    oh it'd be c then or a.

  21. ash2326
    • 3 years ago
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    What did you get for AB?

  22. abm1995
    • 3 years ago
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    8.3?

  23. ash2326
    • 3 years ago
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    Yes, we don't know which is the second side AB or AC. So we can get either 8.3 or 5.8

  24. abm1995
    • 3 years ago
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    so , d?

  25. ash2326
    • 3 years ago
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    yes, did you understand?

  26. abm1995
    • 3 years ago
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    yes! your a lot of help!

  27. ash2326
    • 3 years ago
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    No Problem :)

  28. abm1995
    • 3 years ago
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    i need help with a little more../: i'm behind in school. could you help me?

  29. abm1995
    • 3 years ago
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    What is the value of x?

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  30. abm1995
    • 3 years ago
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    a. 5 b. 2.5 c. 7.5 d. 10

  31. ash2326
    • 3 years ago
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    The two lines indicated with arrow are parallel, so the two triangles are similar

  32. abm1995
    • 3 years ago
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    yes. i know.

  33. ash2326
    • 3 years ago
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    \[\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}\] Now solve for x

  34. abm1995
    • 3 years ago
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    wouldn't it be 5 though?

  35. ash2326
    • 3 years ago
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    yes, just plugin the value and check

  36. abm1995
    • 3 years ago
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    ok, so my answer would be a 5?

  37. ash2326
    • 3 years ago
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    check it, you should ascertain it yourself

  38. abm1995
    • 3 years ago
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    i don't think it's 5.

  39. ash2326
    • 3 years ago
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    What did you get when you plugged in x=5 ?

  40. abm1995
    • 3 years ago
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    idk. i'm just trying to get this done. i'm so behind.

  41. ash2326
    • 3 years ago
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    Relax and do this \[\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}\] \[\frac {x}{2x+5}=\frac{x-2}{2x-1}\] Put x=5 and check

  42. abm1995
    • 3 years ago
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    i got 1/3

  43. ash2326
    • 3 years ago
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    Both sides?

  44. abm1995
    • 3 years ago
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    yes. do you know the answer?

  45. ash2326
    • 3 years ago
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    So 5 is the correct answer

  46. abm1995
    • 3 years ago
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    do you know that it is?

  47. ash2326
    • 3 years ago
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    yes, that's why we got the same thing on both sides. Check other options also, you'll see that the left side won't be equal to the right side

  48. abm1995
    • 3 years ago
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    What similarity statement can you write relating the three triangles in the diagram below?

  49. abm1995
    • 3 years ago
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