## abm1995 Group Title 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. one year ago one year ago

1. ash2326 Group Title

Do you have a figure?

2. abm1995 Group Title

there's no figure. /: sorry.

3. ash2326 Group Title

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 Group Title

yes!

5. ash2326 Group Title

@abm1995 ??

6. abm1995 Group Title

do you want the choices?

7. abm1995 Group Title

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 Group Title

does anyone understand this?

9. ash2326 Group Title

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 Group Title

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

11. abm1995 Group Title

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

12. ash2326 Group Title

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

13. abm1995 Group Title

ok.

14. ash2326 Group Title

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 Group Title

oh ok.

16. abm1995 Group Title

wouldn't the answer be B then?

17. ash2326 Group Title

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

18. abm1995 Group Title

so b?

19. ash2326 Group Title

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

20. abm1995 Group Title

oh it'd be c then or a.

21. ash2326 Group Title

What did you get for AB?

22. abm1995 Group Title

8.3?

23. ash2326 Group Title

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 Group Title

so , d?

25. ash2326 Group Title

yes, did you understand?

26. abm1995 Group Title

yes! your a lot of help!

27. ash2326 Group Title

No Problem :)

28. abm1995 Group Title

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

29. abm1995 Group Title

What is the value of x?

30. abm1995 Group Title

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

31. ash2326 Group Title

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

32. abm1995 Group Title

yes. i know.

33. ash2326 Group Title

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

34. abm1995 Group Title

wouldn't it be 5 though?

35. ash2326 Group Title

yes, just plugin the value and check

36. abm1995 Group Title

ok, so my answer would be a 5?

37. ash2326 Group Title

check it, you should ascertain it yourself

38. abm1995 Group Title

i don't think it's 5.

39. ash2326 Group Title

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

40. abm1995 Group Title

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

41. ash2326 Group Title

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 Group Title

i got 1/3

43. ash2326 Group Title

Both sides?

44. abm1995 Group Title

yes. do you know the answer?

45. ash2326 Group Title

So 5 is the correct answer

46. abm1995 Group Title

do you know that it is?

47. ash2326 Group Title

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 Group Title

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

49. abm1995 Group Title