The length of the room is

The width of the room is

The image below illustrates the question
The side of the room should have a 1-meter border, this means that on both sides of the room,the length and breadth of the room will be reduced by 2 meter
Hence,
The length of the carpet will be

The width of the carpet will be

The area of the uncovered part will be

The area of the room is

The area of the carpet will be

Hence,
the area of the uncovered part will be

Therefore,
k+3 represents the length of the carpet
The final answer is OPTION B