Question

A room of a house is k meters wide and (k+5)meters long. A carpet is to be laid on the floor so that there will be a 1-meter border left all around the room. The uncovered area of the floor can be represented by the expression: k(k+5)−[(k+3)(k−2)] What does (k+3) represent? Athe width of the carpetBthe length of the carpetCthe width of the uncovered areaDthe length of the uncovered area

Answer 1

The length of the room is

`=k+5`

The width of the room is

`=k`

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

`\begin{gathered} =\text{length of the room - 2} \\ =k+5-2 \\ =k+3 \end{gathered}`

The width of the carpet will be

`\begin{gathered} =\text{width of the room}-2 \\ =k-2 \end{gathered}`

The area of the uncovered part will be

`=\text{area of the room - area of the carpet}`

The area of the room is

`\begin{gathered} =\text{length of room}*\text{width of room} \\ =k(k+5) \end{gathered}`

The area of the carpet will be

`\begin{gathered} =\text{length of carpet}* width\text{ of carper} \\ =(k+3)(k-2) \end{gathered}`

Hence,

the area of the uncovered part will be

`=k(k+5)-(k+3)(k-2)`

Therefore,

k+3 represents the length of the carpet

The final answer is OPTION B