## A community for students. Sign up today

Here's the question you clicked on:

## SugarMochi one year ago Someone please help me with this similarity question.

• This Question is Closed
1. SugarMochi

|dw:1444461992182:dw|

2. SugarMochi

The ratio of AB:BC is 1:3 The difference between AE and DE is 4 The ratio of AD to AC is 2:3 AE is 18 and BC is double AE If CD is 52, what is K

3. madhu.mukherjee.946

did you try anything?

4. SugarMochi

I'm confused with the question overall and the topic 'similarities' ;-;

5. anonymous

try solve all the angles. |dw:1444462802038:dw|

6. anonymous

i'll explain these lengths

7. anonymous

We know CD=52 AE =18 BC=2AE=2*18=36 Now the ratio of AB:BC is 1:3 Therefore AB=1/3 *BC=1/3 * 36 = 12 The ratio of AD to AC is 2:3 therefore AD= 2/3 * AC = 2/3 *(36+12) = 2/3 *48 = 32 Therefore we also know The difference between AE and DE is 4 AD=AE + ED hence ED=AD-AE=32-18 = 14 ( This is a true solution since AE-ED = 4)

8. anonymous

Now we know all our lengths. its just a matter of using similar techniques

9. anonymous

|dw:1444463067640:dw|

10. anonymous

lets find the scale factor. AC/AE = 48/18 = 8/3 AD/AB= 32/12 = 8/3 Hence our scale factor is 8/3

11. anonymous

Therefore CD/BE = 8/3 52/K = 8/3

12. anonymous

$\frac{ 52 }{ K }=\frac{ 8 }{ 3 }$ $K=19.5$

13. anonymous

: )

14. SugarMochi

thanyou so much ;-; This really really saved me

15. anonymous

haha no problem : ) fan me if you need my assistance when ever i'm online

16. SugarMochi

Once again, thanyou so much~ This helped alot! :D

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy