Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.

Correct result:

V =  2514.3938 cm³

Solution:

$$\begin{gathered} u=28\text{ cm } \\ a=3x \\ b=1x \\ c=2x \\ u=\sqrt{a^2+b^2+c^2} \\ {u}^2=(9+1+4)x^2 \\ x=\sqrt{{\displaystyle \frac{u^2}{9+1+4}}}=\sqrt{{\displaystyle \frac{28^2}{9+1+4}}}=2\sqrt{14}\text{ m}\doteq 7.4833\text{ m } \\ a=3\cdot x=3\cdot 7.4833=6\sqrt{14}\text{ m}\doteq 22.4499\text{ m } \\ b=x=7.4833=2\sqrt{14}\text{ m}\doteq 7.4833\text{ m } \\ c=2\cdot x=2\cdot 7.4833=4\sqrt{14}\text{ m}\doteq 14.9666\text{ m } \\ V=a\cdot b\cdot c=22.4499\cdot 7.4833\cdot 14.9666=2514.3938{\text{cm}}^3 \end{gathered}$$

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