SOLUTION: 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 de
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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?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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
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