Cuboid face diagonals

The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio?

The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.

Result

y=

Yes

No

Solution:

$$\begin{gathered} a=5 \\ b=10 \\ c=15 \\ a:b:c=1:2:3 \\ {u}_1=\sqrt{a^2+b^2}=\sqrt{5^2+10^2}=5\sqrt{5}\doteq 11.1803 \\ {u}_2=\sqrt{a^2+c^2}=\sqrt{5^2+15^2}=5\sqrt{10}\doteq 15.8114 \\ {u}_3=\sqrt{b^2+c^2}=\sqrt{10^2+15^2}=5\sqrt{13}\doteq 18.0278 \\ {k}_1=u_1:u_2=11.1803:15.8114\doteq 0.7071 \\ {k}_2=u_3:u_2=18.0278:15.8114\doteq 1.1402 \\ {k}_3=u_3:u_1=18.0278:11.1803\doteq 1.6125 \\ {k}_1,k_2,k_3\mathrm{\ne }1,2,3 \\ y=0 \end{gathered}$$

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