Question

AB=15, BC=x, BD=16, AD=25

Answer 1

If the question is to find x, then use the theorem 1.33 from the book:
Geometry Revisited by Coxeter and Greitzer.
It says:
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides."
Visually, it is like the following:

Guess you can take it from here.

Answer 2

i did that and it told me the answer was wrong

Answer 3

ok now im confused

Answer 4

What did you get for the answer? and please show your calculations.

Answer 5

I did 15/25=x/16

Answer 6

So far so good, go on!

Answer 7

so i got 25x=240

Answer 8

x=9.6

Answer 9

Sorry, I misread the question exactly the same way you did.
It says BC=x, BD=16 (not CD).

Answer 10

Since BC+CD=BD=16
we have CD=16-BC=16-x
The equation is then:
\(\large \frac{15}{25}=\frac{x}{16-x}\)
So you can cross multiply and solve for x.

Answer 11

so 25x=240-x

Answer 12

nope, you need to distribute when you multiply 15 by 16-x
15(16-x)=240=15x

Answer 13

i got it!! th answer is 6!

Answer 14

* 240-15x

Answer 15

thank you

Answer 16

You're welcome! :)
Try to remember the handy formula, it will be useful for other problems.