The perimeter of the rectangle is 11.2 m. One of the sides is 2.4 m larger than the neighboring one. find the area of the rectangle.

Let’s denote the sides of the rectangle by x and y.
According to the condition of the problem, the perimeter of this rectangle is 11.2 m, therefore, the following relation is true:
2 * (x + y) = 11.2.
It is also known that one of the sides is 2.4 m larger than the second, therefore, the following relationship is true:
x = y + 2.4.
We solve the resulting system of equations. Substituting into the first equation the value x = y + 2.4 from the second equation, we get:
2 * (y + 2.4 + y) = 11.2.
We solve the resulting equation:
2 * (2 * y + 2.4) = 11.2;
4 * y + 4.8 = 11.2;
4 * y = 11.2 – 4.8;
4 * y = 11.2 – 4.8;
4 * y = 6.4;
y = 6.4 / 4;
y = 1.6.
Knowing y, we find x:
x = y + 2.4 = 1.6 + 2.4 = 4.
Find the area of ​​this rectangle:
S = x * y = 4 * 1.6 = 6.4 sq.m.
Answer: the area of ​​this rectangle is 6.4 sq.m.