Final answer:
To find the greatest possible width of the rectangle, we use the information provided and solve for x in the equation 2(x + 7 + x) < 152 cm. The solution is x < 34.5, so the greatest possible width is 34 cm.
Step-by-step explanation:
To find the greatest possible width of the rectangle, we need to consider the information given. The length of the rectangle is 7 cm longer than the width, so if we let the width be represented by the variable x, then the length would be x + 7 cm. The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. In this case, P < 152 cm.
Substituting the given values into the formula, we have 2(x + 7 + x) < 152 cm. Simplifying, we get 4x + 14 < 152 cm.
Next, we solve for x by subtracting 14 from both sides of the inequality: 4x < 138. Dividing both sides by 4, we find x < 34.5. Since the width must be a whole number, the greatest possible width of the rectangle is 34 cm.