Question

The length of a room exceeds the breadth by $2$ metres. If both the length and the breadth are increased by $1$ metre, then the area of the room is increased by $11$ sq. m. Find the length and the breadth of the room.

• A. $3m$ and $2m$
• B. $2m$ and $7m$
• C. $7m$ and $9m$
• D. $6m$ and $4m$

Answer 1

Answer: (D)

$6m$ and $4m$

Let the breadth of room is $x$ meter

Then length of room = $x+2$ (given)

Then area of room = $(x+2)x$ sq meter

If length and breadth increased $1$ meter

Then length = $(x+2)+1=x+3$ meter and breadth =$x+1$ meter

Then area of new room =$(x+3)(x+1)$ Sq m

As per given in question

$(x+3)(x+1)-(x+2)x=11$

$\Rightarrow x^2+4x+3-x^2-2x=11$

$\Rightarrow 4x-2x=11-3$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

So breadth of room = $4$

And length of room = $4+2=6$