A3. Peter covered a wound with 2 rectangular bandages (see the figure). The area of the region covered by both bandages at the same time is $40 \mathrm{~cm}^{2}$, and the perimeter of the region covered by both bandages at the same time is $30 \mathrm{~cm}$. The upper bandage is $8 \mathrm{~cm}$ wide. How many centimeters is the lower bandage wide?

![](https://cdn.mathpix.com/cropped/2024_06_07_21f8af0300261b15ee68g-02.jpg?height=183&width=342&top_left_y=1822&top_left_x=1551)
(A) 3
(B) 4
(C) 5
(D) 6
(E) 16
A3. The area covered by both parallelograms has the shape of a parallelogram. Let's denote the sides of the parallelogram by $a$ and $b$, and with $x$ the side of the lower parallelogram, whose length we are looking for (see figure).

![](https://cdn.mathpix.com/cropped/2024_06_07_21f8af0300261b15ee68g-18.jpg?height=180&width=334&top_left_y=1572&top_left_x=861)

Then, $a \cdot x = b \cdot 8 = 40 \mathrm{~cm}^{2}$ and $2 a + 2 b = 30 \mathrm{~cm}$. It follows that $b = \frac{1}{8} \cdot 40 = 5 \mathrm{~cm}, a = \frac{1}{2}(30 - 2 \cdot 5) = 10 \mathrm{~cm}$ and $x = \frac{1}{10} \cdot 40 = 4 \mathrm{~cm}$.