# How will the area of a rectangle change if its length is increased by 25%, and its width is reduced by 20%.

1. Let X be the length of the rectangle.

Y is the width of the rectangle.

Then the area is S1 = X * Y.

2. According to the condition of the problem, the length of the rectangle was increased by 25%.

25% = 25/100 = 1/4.

So the new length is X + X * 1/4 = X * (1 + 1/4) = X * 5/4.

3. The width of the rectangle has been reduced by 20%.

20% = 20/100 = 1/5.

The new width is Y – Y * 1/5 = Y * (1 – 1/5) = Y * 4/5.

4. Let’s define a new area.

S2 = X * 5/4 * Y * 4/5 = X * Y * 20/20 = S1 * 1 = S1.

That is, it is equal to the previous area.

Answer: The area of the rectangle will not change.

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