The length of the room is
[tex]=k+5[/tex]The width of the room is
[tex]=k[/tex]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
[tex]\begin{gathered} =\text{length of the room - 2} \\ =k+5-2 \\ =k+3 \end{gathered}[/tex]The width of the carpet will be
[tex]\begin{gathered} =\text{width of the room}-2 \\ =k-2 \end{gathered}[/tex]The area of the uncovered part will be
[tex]=\text{area of the room - area of the carpet}[/tex]The area of the room is
[tex]\begin{gathered} =\text{length of room}\times\text{width of room} \\ =k(k+5) \end{gathered}[/tex]The area of the carpet will be
[tex]\begin{gathered} =\text{length of carpet}\times width\text{ of carper} \\ =(k+3)(k-2) \end{gathered}[/tex]Hence,
the area of the uncovered part will be
[tex]=k(k+5)-(k+3)(k-2)[/tex]Therefore,
k+3 represents the length of the carpet
The final answer is OPTION B
