The greatest possible value for the width is 8 centimeters.
If the width of rectangle is w and given that the length of a rectangle is five times its width.
Then, the length of rectangle [tex]=5w[/tex]
Perimeter of rectangle is,
[tex]Perimerer=2(length+width)\\\\Perimeter=2(5w+w)=12w[/tex]
Since, if the perimeter is at most 96 centimeters.
the greatest possible value for the width is,
[tex]12w\leq 96\\\\w\leq \frac{96}{12}\\ \\w\leq 8[/tex]
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