Dimensions - crate

A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this situation?

Correct answer:

x =  8.6023 m

Step-by-step explanation:

$$\begin{gathered} a=10\text{m} \\ b=4\text{m} \\ c=3\text{m} \\ d=3\text{m} \\ e=4\text{m} \\ f=3\text{m} \\ w=a-d=10-3=7\text{m} \\ {x}^2=w^2+b^2+c^2 \\ x=\sqrt{w^2+b^2+c^2}=\sqrt{7^2+4^2+3^2}=\sqrt{74}=8.6023\text{m} \end{gathered}$$

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