Question 148802
If each dimension of room is increased one meter, the area is increased by 51 meters; and if the length is increased one meter and the width diminished by one meter, the area is decreased three square meters. Find the dimensions of the room?
.
Let L = length of room
and W = width of room
.
(L+1)(W+1)= LW + 51  
(L+1)(W-1)= LW - 3  
.
(L+1)(W+1)= LW + 51
LW+W+L+1= LW + 51
W+L+1 = 51
W+L = 50
.
(L+1)(W-1)= LW - 3
LW+W-L-1= LW - 3
W-L-1= -3
W-L = -2
.
W+L = 50  <<---equation 1
W-L = -2   <<---equation 2
.
Solving equation 2 to W we get:
W-L = -2
W = -2+L
.
Substitute the above into equation 1 and solve for L:
W+L = 50
-2+L+L = 50
2L = 52
L = 26 meters
.
Substitute the above into equation 2 and solve for W:
W-L = -2
W-26 = -2
W = 24 meters
.
Therefore, the dimensions are 26 by 24 meters