How many rectangles of 36 cm perimeter can be drawn, given that sides are positive integers in cm ?

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
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