If the length of a rectangle increases by 4cm and the width decreases by 1cm, the area remains unchanged; if the length decreases by 2cm and the width increases by 1cm, the area remains unchanged, the area of the rectangle is______ ．

Let the length of the rectangle be xcm and the width be YCM. According to the meaning of the question, we get (x + 4) (Y − 1) = XY (x − 2) (y + 1) = XY. The solution is x = 8y = 3, so xy = 8 × 3 = 24. Answer: the area of the rectangle is 24cm2. So the answer is 24cm2

It is known that if the length of a rectangle increases by 3cm and the width decreases by 1cm, the area remains unchanged. If the length decreases by 2cm and the width increases by 4cm, the area also remains unchanged
Find the area of the original rectangle

Let X be length and y be width
(x + 3) (Y-1) = xy-x + 3y-3 = XY, then: - x + 3Y = 3
(X-2) (y + 4) = XY, XY + 4x-2y-8 = XY, then 4x-2y = 8
The solution is: x = 3
y=2
So the area of the original rectangle is 6

The problem of linear inequality of one variable: the area of a rectangle remains unchanged when its length increases by 4cm and its width decreases by 1cm; the area remains unchanged when its length decreases by 2cm and its width increases by 1cm

Let the length be x cm and the width be y cm
xy=(x+4)(y-1) -> 4y-x=4
xy=(x-2)(y+1) -> x-2y=2
The solution is x = 8, y = 3
The area is 8 × 3 = 24 square centimeters