## mathmath333 one year ago Counting Problem

1. anonymous

1, 2, 3, 4 ...

2. mathmath333

25 grey dots 5 blue

6 green lines 5 red

20 squares

6. mathmath333

|dw:1440255088214:dw|

7. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{The red and green lines are parallel to eachother.}\hspace{.33em}\\~\\ & \normalsize \text{Find the number of parallelograms formed.}\hspace{.33em}\\~\\ \end{align}}

i think its still 20 parralelograms

9. anonymous

there is a technique we can use

10. anonymous

btw, how did you draw it like that? it looks cool

a parralleogram is a shape with opposite sides parallel and opposite angles equal

12. mathmath333

Using geozebra

13. mathmath333

|dw:1440255355482:dw|

so is it 20?

15. mathmath333
16. mathmath333

|dw:1440255407583:dw| this is also a prallelogram so answer is not 20

oh

18. ganeshie8

|dw:1440255451325:dw|

19. ganeshie8

To form a parallelogram, you need to choose any 2 red lines and any 2 green lines

20. mathmath333

is their a predefined formula

21. ganeshie8

its not formula as such, you can see that there are 5 red lines, how many ways can you choose 2 red lines ?

22. mathmath333

but why r u choosing 2 red line

23. mathmath333

and 2 grren lines

24. ganeshie8

how many sides are there in a parallelogram ?

25. ytrewqmiswi

a(a -1) x b(b -1) =number of parallelograms m nd n are the number of lines :)

26. mathmath333

4

27. ganeshie8

|dw:1440255729752:dw|

28. ganeshie8

first convince yourself that you must choose exactly 2 red lines and 2 green lines to form a parallelogram

29. mathmath333

ok it forms only 1 parellelofram

30. ganeshie8

try some examples picking different pairs of lines

31. ytrewqmiswi
32. mathmath333

ok i get it

33. mathmath333

34. ytrewqmiswi

yes :)

35. mathmath333