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Given:
Let 'l' and 'w' be the length and width of the swimming pool.
[tex]w=l-13[/tex][tex]\begin{gathered} \text{Perimeter of the swimming pool =2(l+b)} \\ 98=2\lbrack l+l-13\rbrack \\ \frac{98}{2}=2l-13 \\ 49=2l-13 \\ 49+13=2l \\ 62=2l \\ l=31\text{ m} \end{gathered}[/tex][tex]\begin{gathered} w=l-13 \\ w=31-13 \\ w=18\text{ m} \end{gathered}[/tex]Length of the swimming pool is 31m
width of the swimming pool is 18m.