Question 148801
length of the room = x
width of the room = y
If each dimension of room is increased one meter, the area is increased by 51 meters

then (x+1)(y+1)=xy+51

if the length is increased one meter and the width diminished by one meter, the area is decreased three square meters

(x+1)(y-1)=xy-3 so equations are:


(x+1)(y+1)=xy+51
(x+1)(y-1)=xy-3

xy+x+y+1=xy+51
xy-x+y-1=xy-3

x+y+1=51
-x+y-1=-3

adding equations

2y=48 then y=24

x+24+1=51 then x+25=51 then x=26

Answer:Length=26 meters and width=24 meters