Answer:
See attachment
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of all the sides of the rectangle, so it is given by:
[tex]p=2L+2w[/tex]
where
L is the length
w is the width
In this problem, we want to find all the integer values of L and w such that the perimeter is 16 cm:
[tex]p=16 cm[/tex]
This means:
[tex]16=2L+2w[/tex]
Or:
[tex]16=2(L+w)\\\rightarrow L+w=8[/tex]
We have only 4 possible combinations:
L = 7 cm, w = 1 cm
L = 6 cm, w = 2 cm
L = 5 cm, w = 3 cm
L = 4 cm, w = 4 cm
The other combinations with L and w swapped are identical, so we don't include them; therefore, these are the only 4 possible combinations. The 4 possible rectangles are therefore draw in attachment.
