Question

if the length and the breadth of a room are increased by 1 metre,the area is increased by 21 square metres.If the length is increased by 1 metre and breadth is decreased by 1 metre,the area is decreased by 5 square metres.find the perimeter of the room..please briefly

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

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