The length of the rectangle was reduced by 2.4 meters, and the width was increased by 30%.

The length of the rectangle was reduced by 2.4 meters, and the width was increased by 30%. As a result, the area of the new rectangle was 4% larger than the old one. What is the new length of the rectangle?

The area of a rectangle is equal to the product of its length and width.

Let’s introduce variables. Let m be the length of the rectangle, n the value of the width of the rectangle.

The area is equal to:

S = m * n;

The length was increased by 2.4 meters, the width was shortened by 30%, which means that the area became equal to:

S1 = (m – 2.4) * (1.3 * n);

At the same time, the area S1 became equal to:

S1 = 1.04 * m * n;

We equate the right-hand sides of the two equalities:

(m – 2.4) * 1.3 * n = 1.04 * m * n;

1.3 * m * n – 3.12 * n = 1.04 * m * n;

0.26 * m * n = 3.12 * n;

0.26 * m = 3.12;

m = 12;

m – 2.4 = 9.6 m.

Answer: 9.6 m.