abm1995 2 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.

1. ash2326

Do you have a figure?

2. abm1995

there's no figure. /: sorry.

3. ash2326

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

yes!

5. ash2326

@abm1995 ??

6. abm1995

do you want the choices?

7. abm1995

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

does anyone understand this?

9. ash2326

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

no i don't./: i'm dumb.

11. abm1995

do you know the answer? then when i figure it out you will say if i'm right or not?

12. ash2326

Yeah, I'll do let me explain you angle bisector theorem

13. abm1995

ok.

14. ash2326

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

oh ok.

16. abm1995

wouldn't the answer be B then?

17. ash2326

here we have BD=6 DC=5 Now assume AB as 6.9, find AC ???

18. abm1995

so b?

19. ash2326

No not yet. We have to find one more thing, assume AC=6.9 and find AB

20. abm1995

oh it'd be c then or a.

21. ash2326

What did you get for AB?

22. abm1995

8.3?

23. ash2326

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

so , d?

25. ash2326

yes, did you understand?

26. abm1995

yes! your a lot of help!

27. ash2326

No Problem :)

28. abm1995

i need help with a little more../: i'm behind in school. could you help me?

29. abm1995

What is the value of x?

30. abm1995

a. 5 b. 2.5 c. 7.5 d. 10

31. ash2326

The two lines indicated with arrow are parallel, so the two triangles are similar

32. abm1995

yes. i know.

33. ash2326

$\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}$ Now solve for x

34. abm1995

wouldn't it be 5 though?

35. ash2326

yes, just plugin the value and check

36. abm1995

ok, so my answer would be a 5?

37. ash2326

check it, you should ascertain it yourself

38. abm1995

i don't think it's 5.

39. ash2326

What did you get when you plugged in x=5 ?

40. abm1995

idk. i'm just trying to get this done. i'm so behind.

41. ash2326

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

i got 1/3

43. ash2326

Both sides?

44. abm1995

yes. do you know the answer?

45. ash2326

So 5 is the correct answer

46. abm1995

do you know that it is?

47. ash2326

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

What similarity statement can you write relating the three triangles in the diagram below?

49. abm1995