Final answer:
The length of the other side of the rectangle must be less than 2 cm to ensure that its perimeter is smaller than that of a 4 cm sided square, which has a perimeter of 16 cm.
Step-by-step explanation:
The question is asking for the length of the other side of a rectangle so that its perimeter is smaller than that of a square with each side measuring 4 cm. To find this, we first need to understand the concept of perimeter: for a rectangle, it is calculated as 2 times the length plus 2 times the width, and for a square, the perimeter is 4 times the length of one side. A square with a side of 4 cm would have a perimeter of 4 x 4 cm = 16 cm.
Since one side of the rectangle is already given as 6 cm, the perimeter of the rectangle is P = 2l + 2w, with l being established as 6 cm. We need w to be such that 2 x 6 cm + 2 x w is less than 16 cm. Rearranging the terms, we get 2w < 16 cm - 12 cm, which simplifies to 2w < 4 cm. Dividing both sides by 2 gives us w < 2 cm.
The length of the other side of the rectangle must be less than 2 cm to ensure that its perimeter is smaller than that of the square which measures 16 cm in perimeter.