how many different rectangles can be made from 12 squares ?

Question

squares are rectangles. squares are all equal.

Answer 1

12 1-12 long by 1 wide
1 2 long by 2 wide
1 3 long by 2 wide
1 4 long by 2 wide
1 5 long by 2 wide
1 6 long by 2 wide
1 3 long by 3 wide
1 4 long by 3 wide

Total 19 different rectangles, including the starting square.
Total 18 different rectangles "made from" 12 squares (not including the square itself)

Answer 2

I'm guessing that you have to use *all* of the squares (if not, this becomes a very messy problem in a big hurry ☺)

OK. Let the sides of each given square be 1 unit. You can make a very 'long and skinny' rectangle that is 1 unit tall by 12 units long. Or you can make one that's 2 units tall by 6 units long. Or one that's 3 units tall and 4 units long. And that's it. There's only 3 possible rectangles to obe made from 12 squares. Note that each rectangle corresponds to one way of 'factoring' 12. That's the 'secret' to being able to calculate this kind of problem.


Doug

Answer 3

you can make 6 rectangles made out of two squares each
you can make 2 rectangles out of 6 rectangles each
you can make 1 rectangle out of 12
you can make one out of 8
you can make1 out of 10
and thats all i can think of at the moment now if your talking in real life each rectangle can be positioned differently and can therefore be looked at from different perspectives but as for on a piece of paper its 11 well thats what i got i dont feel like counting it out or performing calculations right now ask again ill give you an exact number

Answer 4

if you find out how many pairs of factors are in 12 you will have your answer. (1,12) (2,6) and (3,4). so there are 3 rectangles that can be made. a 1 by 12, a 2 by 6 and a 3 by 4.

Answer 5

2 rectangles can be made from 12 sqares..