3rd dimension

The block has a surface of 42 dm² and its dimensions are 3 dm and 2 dm. What is the third dimension?

Correct answer:

c =  3 dm

Step-by-step explanation:

$$\begin{gathered} S=42{\text{cm}}^2 \\ a=3\text{ dm } \\ b=2\text{ dm } \\ S=2(ab+bc+ca) \\ S\mathrm{/}2=ab+bc+ca \\ c=(S\mathrm{/}2-a\cdot b)\mathrm{/}(b+a)=(42\mathrm{/}2-3\cdot 2)\mathrm{/}(2+3)=3\text{ dm} \end{gathered}$$

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