Question

If the length and breadth of a roon are increased by 1m each, its area is increased by 21sq.m If the length is increased by 1m and breadth is decreased by 1m the area of the room is decreased by 5 sq.m what would be the area of the room.

Answer 1

Let the length and breadth of a room be x & y
Area of the room = x * y
When the length and breadth of a room are increased by 1 metre, then the new dimensions of the room would be
Length : x+1
Width : y+1
New area = (x+1)(y+1)
Since the area is increased by 21 metres, therefore
(x+1)(y+1)- xy = 21...........(1)
Further when the length is increased by 1 metre, then the area would be (x+1) * y
Now when the length is increased by 1 metre , the area is dcreased by 5 square metres
(x+1) * y -xy = 21-5............(2)
Simplifying & solving eqns 1 & 2 results in
x=4 and y=16
Perimeter of the room = 2*(Length+width)
= 2*(4+16)
Ans : 40 meter
I guess this is the answer

Answer 2

Let the length and breadth of a room be x & y 
Area of the room = x * y 
When the length and breadth of a room are increased by 1 metre, then the new dimensions of the room would be 
Length : x+1
Width : y+1 
New area = (x+1)(y+1) 
Since the area is increased by 21 metres, therefore 
(x+1)(y+1)- xy = 21...........(1) 

Further when the length is increased by 1 metre, then the area would be (x+1) * y 
Now when the length is increased by 1 metre , the area is dcreased by 5 square metres 
(x+1) * y -xy = 21-5............(2) 
Simplifying & solving eqns 1 & 2 results in
x=4 and y=16 
Perimeter of the room = 2*(Length+width) 
= 2*(4+16) 
Ans : 40 meter 

Hope This Helps :)