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______ ．

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

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