The perimeter of the rectangle is 39.6 cm. The length is 4, 5 times greater than the width. Find the area of the rectangle.

Let’s write a formula to calculate the perimeter of a rectangle:
2 * (a + b) = 39.6, where a is the width of the rectangle, b is the length of the rectangle.
By condition, it is known that the length is 4.5 times greater than the width. Means: a * 4.5 = b.
Substituting into the original formula, we get: 2 * (a + 4.5 * a) = 39.6.
Let’s solve the equation, find the width of the rectangle: 2a + 9a = 39.6.
11a = 39.6.
a = 39.6 / 11 = 3.6 cm.
Find the length of the rectangle: b = 3.6 * 4.5 = 16.2 cm.
Let us now find the area of the rectangle: S = a * b = 3.6 * 16.2 = 58.32 cm².
Answer: the area of the rectangle is 58.32 cm².