4. A square with an area of $400 \mathrm{~cm}^{2}$ is divided by two lines into two squares and two rectangles. Calculate the perimeter of each square and each rectangle, if the lengths of the adjacent sides of the two rectangles differ by $60 \mathrm{~mm}$.
4. It is necessary to equalize the units of measurement in the task, for example, convert millimeters to centimeters:

$60 \mathrm{~mm}=6 \mathrm{~cm}$

The area of the given square is $400 \mathrm{~cm}^{2}$, so the length of the side of this square is $20 \mathrm{~cm}$.

![](https://cdn.mathpix.com/cropped/2024_05_30_d90708e9bb68f4d725c6g-4.jpg?height=708&width=766&top_left_y=1208&top_left_x=288)

The lengths of the sides are correctly marked (they can be marked with two different labels, but it must be indicated that one side is longer than the other by $6 \mathrm{~cm}$):

1 POINT

(Note: The given labels can be on the sketch or outside the sketch.)

Given the labels as in the image, the following holds:
$a+(a+6)=20$
1 POINT

$2 a=14 \Rightarrow a=7 \mathrm{~cm}$

1 POINT

For the square AEIH, it holds:

$o_{1}=4 \cdot(a+6)=4 \cdot 13=52 \mathrm{~cm}$

For the square IFCG, it holds:

$o_{2}=4 \cdot a=4 \cdot 7=28 \mathrm{~cm}$

From the sketch, it is clear that the rectangles HIGD and EBFI have corresponding sides of equal length, so they have equal perimeters.