The length of the rectangle is 4 times the width, the length of the rectangle was reduced by 10%

The length of the rectangle is 4 times the width, the length of the rectangle was reduced by 10% and the width and increased by 10% by what percentage of the area of the rectangle changed

Let’s say that the width of the rectangle is a.

The length is 4 times the width, that is, equal to 4 * a.

So the area of the rectangle is:

S = 4 * a * a = 4 * a².

The length of the rectangle was reduced by 10%, which means it was:

4 * a * (100 – 10): 100 = 3.6 * a.

The width was increased by 10% and it was:

a * (100 + 10): 100 = 1.1 * a.

The area of the rectangle became equal to:

S = 3.6 * a * 1.1 * a = 3.96 * a².

Thus, the area of the rectangle has decreased by:

(4 * a² – 3.96 * a²): 4 * a² * 100 = 0.04: 4 * 100 = 1%.