The correct answer is (b), 9.
To solve this, we can use the following formula:
$P = 2l + 2w$
where $P$ is the perimeter, $l$ is the length, and $w$ is the width.
We know that $P = 36$, so we can plug that in to the formula:
$36 = 2l + 2w$
$18 = l + w$
Now, we can try different values for $l$ and $w$ to see if we can find any combinations that add up to 18.
We know that $l$ and $w$ must both be positive integers, so we can start with the smallest possible values, which are 1 and 18.
$1 + 18 = 19$
This doesn’t work, so we can try the next smallest values, which are 2 and 16.
$2 + 16 = 18$
This works! So, one possible rectangle is 2 cm by 16 cm.
We can keep trying different values for $l$ and $w$ until we find all of the possible combinations.
Here are all of the possible rectangles of 36 cm perimeter:
- 2 cm by 16 cm
- 3 cm by 12 cm
- 4 cm by 10 cm
- 5 cm by 9 cm
- 6 cm by 8 cm
- 7 cm by 7 cm
- 8 cm by 6 cm
- 9 cm by 5 cm
- 10 cm by 4 cm
- 12 cm by 3 cm
- 16 cm by 2 cm
There are a total of 9 possible rectangles.