According to the perimeter of the rectangle, it is found that it's greatest possible width is of 34 cm.
What is the perimeter of a rectangle?
The perimeter of a rectangle of length l and width w is given by:
[tex]P = 2(l + w)[/tex]
In this problem, the length of the rectangle is 7cm longer than the width, hence l = 7 + w. Considering that the perimeter is less than 152 cm:
[tex]2(l + w) < 152[/tex]
[tex]l + w < 76[/tex]
[tex]7 + w + w < 76[/tex]
[tex]2w < 69[/tex]
[tex]w < 34.5[/tex]
Rounding, it's it's greatest possible width is of 34 cm.
More can be learned about the perimeter of a rectangle at https://brainly.com/question/10489198