the length+width must be 8.
So, how many pairs of numbers add to 8?
1+7
2+6
...
How many rectangles can be drawn with perimeter of each rectangle as 16 cm?
2 answers
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.
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.