One of the most important and exam oriented question from linear equations in two variables in which we have been asked to find the length and breadth of a room if its length is 3 m more than its breadth and if its length increases by 3 m and breadth decreases by 2 m, it’s area remains unaffected

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 38

## Let the breadth of the room beÂ xÂ m.

Therefore, lengthÂ =x+3Â m

According to the given condition,

x(x+3)=(3+x+3)(xâˆ’2)

3x+x2=(6+x)(xâˆ’2)

3x+x2=6xâˆ’12+x2âˆ’2x

x=12

Therefore, length =Â x+3=15m

Breadth =Â x=12m