The perimeter of the rectangle is 4m 8 dm, one of its old is 5 times larger than the adjacent side, find the area of the rectangle.

Let’s find the lengths of the sides of this rectangle.
Let’s denote by x the length of the shorter side of this rectangle.
According to the condition of the problem, one of the sides of this rectangle is 5 times larger than the neighboring side, therefore, the length of the larger side of this rectangle is 5x.
It is also known that the perimeter of this rectangle is 4m 8 dm, which in meters is:
4m + 0.8m = 4.8m.
The perimeter of any rectangle is equal to twice the sum of the length and width of this rectangle, therefore, we can make the following equation:
2 * (5x + x) = 4.8.
We solve the resulting equation:
2 * 6x = 4.8;
12x = 4.8;
x = 4.8 / 12;
x = 0.4 m.
Knowing the length of the smaller side of a given rectangle, we find the length of its larger side:
5 * x = 5 * 0.4 = 2 m.
Find the area S of this rectangle:
S = 2 * 0.4 = 0.8 m².
Answer: the area of ​​this rectangle is 0.8 m².