Question

Look at the figure below.



What is the value of x?

Answer 1

triangle AFD ~ triangle ACB (AAA)
\[\frac{4}{11} = \frac{x+2}{(x+2)+14} (corr. \ sides, \ similar\triangle s\]
Can you solve it?

Answer 2

no i dont understand

Answer 3

Hmm... which part?

Answer 4

so 4/11 turns in x+2/(x+2)+14?

Answer 5

Hmm.. these are the ratio.
For similar triangles, the ratio of a pair of corresponding sides are the same for all the 3 pairs
Got this part?

Answer 6

yeah i think

Answer 7

sorry been testing for days bare with me xD

Answer 8

Never mind :)
And which part you don't understand now?

Answer 9

How do i solve the equation. I mean i know it's not about getting the answer so maybe you could go through it with me

Answer 10

I've done pretty good on the test so far i just never got these lol

Answer 11

Hmm... do you know how to set up that equation?

Answer 12

What do you mean by that?

Answer 13

4/11=2x/2x+14?

Answer 14

it's x+2 .... instead of 2x...

Answer 15

ah k but what is x+2=?

Answer 16

Sorry for not being here for a while...
x+2 is AD in your diagram

Answer 17

Do you know triangle AFD ~ triangle ACB ?

Answer 18

yeah

Answer 19

So,
\[\frac{AF}{AC} = \frac{AD}{AB}\]corr. sides, ~ triangles
That's what we've used to set up that equation.

Answer 20

oh ok and how do you solve it? do you just plug in numbers?

Answer 21

Put the number or expression in it.

Answer 22

4/11 = x+2/(x+2)+14

Answer 23

i still don't know how to solve it lol if you can't add the x to the 2 then what do i do?

Answer 24

\[\frac{4}{11} =\frac{x+2}{(x+2)+14}\]First, simplify the denominator of fraction on the right side

Answer 25

5.5 lol?

Answer 26

Eh... I really mean the denominator... you need to use cross multiplication in this case
\[\frac{4}{11} =\frac{x+2}{(x+2)+14}\]\[\frac{4}{11} =\frac{x+2}{x+16}\]\[4(x+16) = 11(x+2)\]Got it so far?

Answer 27

yeah

Answer 28

one sec im working it

Answer 29

does this come next 4x+64=11x22?

Answer 30

4x+64=11x+22

Answer 31

yeah i mean that sorry :)

Answer 32

Yes!~ and then?

Answer 33

subtract 22 from both sides? I always forget with which side to start first

Answer 34

Yes

Answer 35

4x+42=11x ?

Answer 36

Then you divide both sides by 4?

Answer 37

it becomes 42=2.75x?

Answer 38

idk i mest up somewhere cause idk

Answer 39

Nope..
For 4x+42=11x
subtract 4x from both sides

Answer 40

oh

Answer 41

the answer is 6?

Answer 42

Yes

Answer 43

thanks sorry it took so long ;/

Answer 44

I'm sorry.... that I kept you waiting :|