4. The perimeter of a rectangle is 48 cm, and its length is 2 cm more than its width. Find the area of this rectangle.
4. This problem can be solved both analytically and arithmetically.

First method of solving.

According to the condition

$$
(a+b) \times 2=48
$$

from this we can conclude that $a+b=24$.

Using the second condition $a=b+2$, we get an equation to determine $b$:

$$
b+2+b=24, 2b=22, b=11(\mathrm{~cm})
$$

From the condition $a=b+2$ we find the value of $a(a=13)$.

Multiplying the values of $a$ and $b$, we get the area of the rectangle.

$$
S=13 \times 11=143\left(\mathrm{~cm}^{2}\right)
$$

Second method of solving.

We will make a brief record of the problem condition in the form of a drawing:

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-042.jpg?height=360&width=1214&top_left_y=260&top_left_x=415)