Question

RS=6, RT=3, and TS=4 1/2. Find MR.

Answer 1

Well, from the given can you determine anything else?

Answer 2

Umm .like I'm not sure if from the given I need everything in it?
I know it might be like two seperate equations

Answer 3

Because TS:RS = TS:SM right?

Answer 4

If you know they are similar triangles, then yes, you can use rations to sove it.

Answer 5

Well like the whole section of the book is on similar triangles .

Answer 6

This isn't a proof so I think it's assumed they're similar ?

Answer 7

Well, you can probably show they are using the given angle that is congruent.

Answer 8

But lets just say they are. Then yes, you can make a ratio between them and find all the sides.

Answer 9

So first I need to solve that. Like\[\frac{ 6 }{ 4.5 } = \frac{ SM }{ 4.5 }\]

Answer 10

Oops wait.

Answer 11

\[\frac{ 6 }{ 4.5 } = \frac{ 4.5 }{ SM }\]

Answer 12

because ST is mean proportional ?

Answer 13

Yah, that should work. And once you know the whole side, subtract off the excess.

Answer 14

That would be 6SM=20.25?
then divide ?

Answer 15

Hmmm.... but it gives an odd number.

Answer 16

Maybe turn it into a fraction\[6SM = 20 \frac{ 1}{ 4 }\]

Answer 17

\[6SM = \frac{ 81 }{ 4 } , SM = \frac{ 81 }{ 24 }\]

Answer 18

Now we need to do the proportion of TR?

Answer 19

Note: It is the longest side. Therefore it must be more than 6 because 6 is part of it....

Answer 20

Okay but now we do this?
\[\frac{ MR }{ 3 } = \frac{ 3 }{ 6 }\]

Answer 21

No. You have found MS=3.375. That is impossible.

Answer 22

lol. idk.
Maybe you can assume the picture to be like how the numbers are?

Answer 23

Well, I am not sure you have identified what is similar properly. That makes it hard to get the right answer.

Answer 24

Is not TM the bisector of angle PTR? Idk if that helps

Answer 25

Yes, it is... hmmm....

Answer 26

I'm looking up notes seeing if I can figure this with you

Answer 27

a theorem says the bisector of exterior angle of triangles divides opposite side externally into segment which have some ratio as other 2 sides.

Answer 28

Ah, found a diragram. You may have a direct ratio:
http://jwilson.coe.uga.edu/emt725/Bisect/bisect.html

Answer 29

On that one, it shows constructing:
\(\dfrac{AD}{BD}=\dfrac{AC}{BC}\)

Now, if you translate that to yours...

Answer 30

OK, so used that info, or another version here:
http://jwilson.coe.uga.edu/MATH7200/SupplementalTheorems/SupplementalTheorems.html
to come up with this:

\(\dfrac{TS}{RT}=\dfrac{MS}{MR}\)

Now, what is known?

\(\dfrac{4.5}{3}=\dfrac{MS}{MR}\)

Does not look too good, two unknowns... BUT!

MS = MR + RS
MS = MR + 6

\(\dfrac{4.5}{3}=\dfrac{MR + 6}{MR}\)

One unknown!

Answer 31

Check the way I put it together with your "bisector of exterior angle of triangles divides opposite side externally into segment which have some ratio as other 2 sides" notes. You should be able to do that or something very similar. I may have a number in the wrong place... so check it! But that will lead to an answer.

Answer 32

So I am guessing you got it.