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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.

Mathematics
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Do you have a figure?
there's no figure. /: sorry.
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?

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Other answers:

yes!
do you want the choices?
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
does anyone understand this?
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?
no i don't./: i'm dumb.
do you know the answer? then when i figure it out you will say if i'm right or not?
Yeah, I'll do let me explain you angle bisector theorem
ok.
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| \[\frac{BD}{DC}=\frac {AB}{AC}\]
oh ok.
wouldn't the answer be B then?
here we have BD=6 DC=5 Now assume AB as 6.9, find AC ???
so b?
No not yet. We have to find one more thing, assume AC=6.9 and find AB
oh it'd be c then or a.
What did you get for AB?
8.3?
Yes, we don't know which is the second side AB or AC. So we can get either 8.3 or 5.8
so , d?
yes, did you understand?
yes! your a lot of help!
No Problem :)
i need help with a little more../: i'm behind in school. could you help me?
What is the value of x?
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a. 5 b. 2.5 c. 7.5 d. 10
The two lines indicated with arrow are parallel, so the two triangles are similar
yes. i know.
\[\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}\] Now solve for x
wouldn't it be 5 though?
yes, just plugin the value and check
ok, so my answer would be a 5?
check it, you should ascertain it yourself
i don't think it's 5.
What did you get when you plugged in x=5 ?
idk. i'm just trying to get this done. i'm so behind.
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
i got 1/3
Both sides?
yes. do you know the answer?
So 5 is the correct answer
do you know that it is?
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
What similarity statement can you write relating the three triangles in the diagram below?
1 Attachment

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