Answer:
The length of the pool is 12.5 m.
Step-by-step explanation:
Length of the Olympic size swimming pool, [tex]L=50\textrm{ m}[/tex]
Width of the Olympic size swimming pool, [tex]W=25\textrm{ m}[/tex]
Width of the similar pool, [tex]w=6.25\textrm{ m}[/tex].
Let the length of the similar pool be [tex]x[/tex] m.
Now, if the two pools are similar, then their corresponding sides are proportional. This gives,
[tex]\frac{x}{L}=\frac{w}{W}\\\\\frac{x}{50}=\frac{6.25}{25}\\\\x=\frac{6.25}{25}\times 50=6.25\times 2=12.5\textrm{ m}[/tex]
Therefore, the length of the similar pool is 12.5 m.
