The perimeter of the rectangle is 54 cm. Its length is 5 cm longer than its width. Find the area of the rectangle.

Let’s denote by x the length of this rectangle, and by y – its width.
According to the condition of the problem, the perimeter of this rectangle is 54 cm, therefore, the following relationship takes place:
2 * (x + y) = 54.
It is also known that the length of this rectangle is 5 cm greater than its width, therefore, the following relationship holds:
x = 5 + y.
We solve the resulting system of equations.
Substituting in the first equation the value x = 5 + y from the second equation, we get:
2 * (5 + y + y) = 54;
2 * y + 5 = 54/2;
2 * y + 5 = 27;
2 * y = 27 – 5;
2 * y = 22;
y = 22/2;
y = 11 cm.
Knowing y, we find x:
x = 5 + y = 5 + 11 = 16 cm.
Find the area S of a given rectangle as the product of the length and width of a given rectangle:
S = 16 * 11 = 176 cm².

the area of ​​the rectangle is 176 cm².