SOLUTION: I 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 dec
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Question 148801: I 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? Found 2 solutions by oscargut, stanbon:Answer by oscargut(2103) (Show Source):
You can put this solution on YOUR website! 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
You can put this solution on YOUR website! If each dimension of a 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?
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Let the original dimensions be x and y.
Original area = xy sq meters
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Change dimensions:
New area - old area = 51
(x+1)(y+1)-xy = 51
(x+1)(y-1) -xy = -3
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Rearrange:
x + y = 50
-x+ y = -2
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Adding you get:
2y = 48
y = 24 (one original dimention)
Then x = 26 (the other original dimention)
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Cheers,
Stan H.
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