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.

- anonymous

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- ash2326

Do you have a figure?

- anonymous

there's no figure. /: sorry.

- 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?

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## More answers

- anonymous

yes!

- ash2326

@abm1995 ??

- anonymous

do you want the choices?

- anonymous

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

- anonymous

does anyone understand this?

- 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?

- anonymous

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

- anonymous

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

- ash2326

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

- anonymous

ok.

- 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|
\[\frac{BD}{DC}=\frac {AB}{AC}\]

- anonymous

oh ok.

- anonymous

wouldn't the answer be B then?

- ash2326

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

- anonymous

so b?

- ash2326

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

- anonymous

oh it'd be c then or a.

- ash2326

What did you get for AB?

- anonymous

8.3?

- ash2326

Yes, we don't know which is the second side AB or AC. So we can get either 8.3 or 5.8

- anonymous

so , d?

- ash2326

yes, did you understand?

- anonymous

yes! your a lot of help!

- ash2326

No Problem :)

- anonymous

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

- anonymous

What is the value of x?

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- anonymous

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

- ash2326

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

- anonymous

yes. i know.

- ash2326

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

- anonymous

wouldn't it be 5 though?

- ash2326

yes, just plugin the value and check

- anonymous

ok, so my answer would be a 5?

- ash2326

check it, you should ascertain it yourself

- anonymous

i don't think it's 5.

- ash2326

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

- anonymous

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

- 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

- anonymous

i got 1/3

- ash2326

Both sides?

- anonymous

yes. do you know the answer?

- ash2326

So 5 is the correct answer

- anonymous

do you know that it is?

- 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

- anonymous

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

- anonymous

##### 1 Attachment

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