Block dimension ratio

The block's dimensions are in the ratio 16:12:8, and the sum of these dimensions is 240 decimetres. What are the dimensions of the block?

Final Answer:

a =  106.6667 dm
b =  80 dm
c =  53.3333 dm

Step-by-step explanation:

$$\begin{gathered} a:b:c=16:12:8 \\ s=240\text{dm} \\ x=\frac{s}{16+12+8}=\frac{240}{16+12+8}=\frac{20}{3}\doteq 6.6667\text{dm} \\ a=16\cdot x=16\cdot 6.6667=106.6667\text{dm} \end{gathered}$$

$b=12\cdot x=12\cdot 6.6667=80\text{dm}$

$c=8\cdot x=8\cdot 6.6667=53.3333\text{dm}$

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