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 at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide.
What was the width of the second patch?

Correct result:

v₂ =  4 cm

Solution:

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

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