### Find the length of the longest pole that can be put in a hall of dimensions $13 \space m$ by $12 \space m$ by $5 \space m.$

$18.385 \space m$
\begin {align} l & = 13 \space m \\ b & = 12 \space m \\ h & = 5 \space m \end {align}
2. \begin {align} \text {Length of the longest pole} & = \text {Length of the diagonal} \\ & = \sqrt {l^2 + b^2 + h^2 } \space units \\ & = \sqrt {(13)^2 + (12)^2 + (5)^2} \space m \\ & = \sqrt {169 + 144 + 25} \space m \\ & = \sqrt {338} \space m \\ & = 18.385 \space m \end {align}
3. Therefore, the length of the longest pole that can be put in a hall of dimensions $13 \space m$ by $12 \space m$ by $5 \space m$ is $18.385 \space m$.