Question

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.

Answer 1

Do you have a figure?

Answer 2

there's no figure. /: sorry.

Answer 3

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

Do you understand the figure?

Answer 4

yes!

Answer 5

@abm1995 ??

Answer 6

do you want the choices?

Answer 7

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

Answer 8

does anyone understand this?

Answer 9

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?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

ok.

Answer 14

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

Answer 15

oh ok.

Answer 16

wouldn't the answer be B then?

Answer 17

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

Answer 18

so b?

Answer 19

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

Answer 20

oh it'd be c then or a.

Answer 21

What did you get for AB?

Answer 22

8.3?

Answer 23

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

Answer 24

so , d?

Answer 25

yes, did you understand?

Answer 26

yes! your a lot of help!

Answer 27

No Problem :)

Answer 28

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

Answer 29

What is the value of x?

Answer 30

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

Answer 31

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

Answer 32

yes. i know.

Answer 33

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

Answer 34

wouldn't it be 5 though?

Answer 35

yes, just plugin the value and check

Answer 36

ok, so my answer would be a 5?

Answer 37

check it, you should ascertain it yourself

Answer 38

i don't think it's 5.

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

i got 1/3

Answer 43

Both sides?

Answer 44

yes. do you know the answer?

Answer 45

So 5 is the correct answer

Answer 46

do you know that it is?

Answer 47

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

Answer 48

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