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If each dimension of a room is increased one meter, the area is increased by 51 meters ; and if the length is increased
by one meter and the width diminished by one meter, the area is decreased 3 square meters. Find the dimensions
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(x+1)*(y+1) - xy = 51, (1) (x = the length, y = the width)
(x+1)*(y-1) - xy = -3. (2)
Simplify (by opening the parentheses)
xy + x + y + 1 - xy = 51,
xy - x + y - 1 - xy = -3,
or
x + y = 50, (1')
-x + y = -2 (2')
Add (1') and (2') (both sides). You will get
2y = 48. Then y = = 24. Hence, the width is 24 m.
Then from (1') x = 50-y = 50-24 = 26 m.
Answer. The length is 26 m, the width is 24 m.