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Question

ttp · Answer

@mathstudent55

michele_laino · Answer

If we apply that theorem, we can write this proportion:
$$BF:FC = AE:EC$$
and after a substitution, such proportioon can be rewritten as follows:
$$BF:24 = 12:18$$
Please, apply the fundamental property and compute the value of BF

michele_laino · Answer

I meant the fundamental property of proportions, of course!

ttp · Answer

how do I do that? can you  help me?

mathstudent55 · Answer

I'd like to start the problem from the beginning.
We need to look at each choice to see what each segment measures and to see if it's correct.
We apply the theorem for each choice and solve for the segment of each choice.

Choice A
BD = 12
Using the theorem we have:

$\dfrac{AD}{BD} = \dfrac{AE}{CE} $

$\dfrac{6}{BD} = \dfrac{12}{18}$

$12BD = 6 \times 18= 108$ 

$BD = 9$

Choice A is false.

mathstudent55 · Answer

Choice B
BD = 4
We already know BD = 9, so choice B is also false.

ttp · Answer

ok :)

mathstudent55 · Answer

Choice C
BF = 16

$\dfrac{BF}{CF} = \dfrac{AE}{CE}$

$\dfrac{BF}{24} = \dfrac{12}{18}$

$18BF = 12 \times 24 =288$

$BF = \dfrac{288}{18}$

What do you get for BF?

ttp · Answer

It's true.?

mathstudent55 · Answer

What did you get for BF?
What is 288/18?

mathstudent55 · Answer

Really?
Do it again.
What is 288/18?

ttp · Answer

16. I accidentally did 288/16

mathstudent55 · Answer

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