Determine how the area of the rectangle will change if one of the sides is increased k times

Determine how the area of the rectangle will change if one of the sides is increased k times and the other is reduced k times.

Let initially the sides of the rectangle be equal to x and y. The area of a rectangle is equal to the product of its length and width. In our case, the initial area of the rectangle is x * y.
Now let’s increase the length of the rectangle by k times, it will become equal to k * x. And we will decrease the width of the rectangle by a factor of k, it will become equal to y / k. Let’s write down the area of the resulting rectangle by multiplying its length and width:
k * x * y / k = x * y. The coefficient k is eliminated and the area of the rectangle remains unchanged.
Answer: will not change.