Question

How many rectangles can be drawn with perimeter of each rectangle as 16 cm?

Answer 1

the length+width must be 8.

So, how many pairs of numbers add to 8?

1+7
2+6
...

Answer 2

l = length

w = width

P = 2 ( w + l )

If each side is a whole number, then:


1.

w = 1 , l = 7

P = 2 ( w + l )

P = 2 ( 1 + 7 ) = 2 * 8 = 16

1 x 7


2.

w = 2 , l = 6

P = 2 ( w + l )

P = 2 ( 2 + 6 ) = 2 * 8 = 16

2 x 6


3.

w = 3 , l = 5

P = 2 ( w + l )

P = 2 ( 3 + 5 ) = 2 * 8 = 16

3 x 5


4.

w = 4 , l = 4

P = 2 ( w + l )

P = 2 ( 4 + 4 ) = 2 * 8 = 16

4 x 4


5.

w = 5 , l = 3

P = 2 ( w + l )

P = 2 ( 5 + 3 ) = 2 * 8 = 16

5 x 3


6.

w = 6 , l = 2

P = 2 ( w + l )

P = 2 ( 6 + 2 ) = 2 * 8 = 16

6 x 2


7.

w = 7 , l = 1

P = 2 ( w + l )

P = 2 ( 7 + 1 ) = 2 * 8 = 16

7 x 1



7 x 1 is same 1 x 7

6 x 2 is same 2 x 6

4 x 4 is square

5 x 3 is same 3 x 5


So 3 rectangles:

1 x 7

2 x 6

3 x 5


If each side isn't a whole number, than infinity rectangles can be drawn.