Question

(image below)

If AX:XB as AB:AC, find the missing length.
AX = 5, XB = 4, AC = 6, find AB.
24/5
10/3
15/2

Answer 1

The bisectrix theorem states, and I'll use this triangle as a reference that:
\[\frac{ CA }{ CB }=\frac{ CX }{ XB }\]

Answer 2

oops, make a mistake there:
\[\frac{ AC }{ AB }=\frac{ CX }{ XB }\]

Answer 3

Okay, so it would look like this?

5/4 = ?/6

and I'm guessing that I would have to multiply 5 and 4 leaving me with 20 = ? * 6 ?

Answer 4

Is this ^ correct?

Answer 5

Wait if I am correct wouldn't the answer be 10/3?

Answer 6

I would first use the given relationships in order to rewrite eveything to find the missing and asked-for side.

Answer 7

so is what I put correct? I'm still not sure if I am doing this correct.

Answer 8

Well you are given the relationship:
\[\frac{ AX }{ XB }=\frac{ AB }{ AC }\]
You are given the corresponding sides, am I wrong?
All is just to plot it:
\[\frac{ 5 }{ 4 }=\frac{ AB }{ 6 }\]
now it is just a matter to solve for AB.

Answer 9

Okay, so it would be 5*6 = 4*AB

30 = 4*AB

30/4 = 4/4 *AB

this would leave me with 7.5 = AB, 7.5 as a fraction equals 15/2. so 15/2 is the answer.

Thank you for your help. :)

Answer 10

Great job!