The length of the rectangle was increased by 30%, and its width was decreased by 15%.

The length of the rectangle was increased by 30%, and its width was decreased by 15%. By what percentage has the area of the rectangle increased?

Let us denote by a and to the sides of the original rectangle, then its area S1 will be equal to:

S1 = a * b = ab.

After the changes, the length will be:

a + 30 * a / 100 = 1.3a;

and width:

b – 15 * b / 100 = 0.85b.

The area of the resulting rectangle S1 is equal to:

1.3a * 0.85b = 1.105ab.

The area ratio is:

S1 / S = 1.105ab / ab = 1.105.

Answer: the area will increase by 1.105 times.