Two patches

Peter taped the wound with two rectangular patches (one over the other to form the letter X).
The area sealed with both patches simultaneously had an area of 40cm² and a circumference of 30cm. One of the patches was 8cm wide.
What was the width of the second patch?

Correct answer:

v₂ =  4 cm

Step-by-step explanation:

$$\begin{gathered} S=40{\text{cm}}^2 \\ o=30\text{cm} \\ {v}_1=8\text{cm} \\ S=a{v}_1=b{v}_2 \\ o=2(a+b) \\ a=S/v_1=40/8=5\text{cm} \\ b=o/2-a=30/2-5=10 \\ {v}_2=S/b=40/10\text{cm}=4\text{cm} \end{gathered}$$

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