3rd dimension

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

Result

c =  3 dm

Solution:

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

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