shubhamsrg 3 years ago geometry + similarity question i'd guess.. PQRS is a //gm PS//ZX PZ / QZ = 2/3 find XY/SQ =?

1. CliffSedge

Is there a second parallelogram adjacent to the fist? I'm trying to imagine the scenario.

2. shubhamsrg

|dw:1350050559015:dw|

3. CliffSedge

Ah.

4. CliffSedge

I can start by stating the obvious: SX/QX = 2/3.

5. shubhamsrg

hmm,,yep.. here's what i tried to do.. |dw:1350051162014:dw|

6. shubhamsrg

7. CliffSedge

YM // to XZ? Hmm, yes, possibly..

8. shubhamsrg

yep.. //

9. shubhamsrg

further,, we may also see.. |dw:1350051445715:dw| let PZ = 2l thenZQ = 3l let ZM = j then MQ = 3l -j

10. shubhamsrg

|dw:1350051539893:dw| we can easily see a/(a+b+c) = 2/5 b/(a+b+c)= j/5l c/(a+b+c) =(3l -j)/5l we need to find numerical value of b/(a+b+c) where, we know that a/(b+c) = 2/3 any help ?

11. sauravshakya

Is it 1/10

12. shubhamsrg

nopes..

13. shubhamsrg

nopes according to my book i mean,,i dont know! :P what was your solution ?

14. ganeshie8

is it 1/3 ?

15. estudier

It's a/5-a whatever that is...:-)

16. shubhamsrg

nopes..not that either..

17. CliffSedge

Here's what I got so far. I let PZ=2 and ZQ=3 since that satisfies the ratio. XQ/ZQ = SX/PZ -> XQ/3 = SX/2 XQ/ZQ = 2/3 -> XQ = 2 SX/PZ = XQ/ZQ -> SX/2 = 2/3 SX = 4/3 SX+XQ = 10/3

18. shubhamsrg

XQ/ZQ = SX/PZ ?? how sir ?

19. CliffSedge

Similar triangles.

20. shubhamsrg

ohh.lol..sorry,,i didnt compare with figure properly that one..hmm..

21. shubhamsrg

XQ/ZQ = 2/3 -> XQ = 2 will that be right to conclude ?

22. shubhamsrg

am saying this since this would be another assumption based on an earlier assumtion that PZ=2 and ZQ = 3

23. CliffSedge

I think so, that's what I got. I'm still playing around with the proportions to find XY or YQ..

24. CliffSedge

That wasn't an assumption, that was an arbitrary choice. There's no restriction on what PZ and ZQ are as long as they satisfy the ratio.

25. shubhamsrg

but, in generailty, we have PZ = 2m and ZQ = 3m you assumed m=1 ,,fair enough now XQ/ZQ = 2/3 XQ = 2n => ZQ = 3n this came from the fact m =1// now will that be right in saying n=1 also when m=1 already ?

26. sauravshakya

Is it 2/5

27. estudier

SY/YQ should be 5/2 I think

28. estudier

Oops no, 5/3

29. CliffSedge

If you're using 2m and 3m and 2n and 3n, just because you can choose m=1 at first, that doesn't make n=1.

30. shubhamsrg

thats what am saying,,but you took both m and n = 1 ..

31. shubhamsrg

neither of those @sauravshakya and @estudier ans is 9/40

32. CliffSedge

I never bothered with m or n at all. I set PZ=2 and ZQ=3 and the rest followed.

33. ganeshie8

gotcha !

34. shubhamsrg

PZ=2 and ZQ = 3 made you reach till XQ/ZQ = 2/3 but XQ = 2 and ZQ=3 i guess wont be right..

35. shubhamsrg

@ganeshie8 am quite eager to know..

36. ganeshie8

$$\triangle YZX \sim \triangle YRQ$$

37. shubhamsrg

oh,,i never really saw that,,cool !

38. estudier

I wasn't saying 5/3 was the answer, I was saying that if RZ divides PQ in ratio 2 to 3 then Y divides SQ in ratio 2+3 to 3 (imagine RZ sliding along QP until it becomes a diagonal of the //gram)

39. ganeshie8

and, $$\frac{ZQ}{PQ} = \frac{3}{5}$$

40. ganeshie8

those two are sufficient to get to 9/40

41. shubhamsrg

am sorry but am still unable to @ganeshie8 :|

42. CliffSedge

I was able to get it using estudier's SY/YQ=5/3. SY + YQ = SQ = 10/3 SY = 10/3 - YQ (10/3-/YQ)/YQ = 5/3 -> YQ=5/4 SY = 25/12 XY = SY-SX -> XY = 3/4 XY/SQ = (3/4)/(10/3) = 9/40. QED.

43. shubhamsrg

ohh,,wait,,leme try again @ganeshie8

44. ganeshie8

ok else id post... :) im seeing estudier posts.. .

45. shubhamsrg

thats really amazing.. gotcha @ganeshie8 @estudier @CliffSedge thanks all..really really great !!