Final answer:
To find the allowed values for x, use the perimeter formula P = 2l + 2w, and set up the inequality 2(45) + 2x ≤ 150. After simplifying and solving for x, the value for x must be less than or equal to 30 centimeters to ensure the perimeter does not exceed 150 centimeters.
Step-by-step explanation:
First, to find the allowed values for x so that the perimeter of a rectangle is no greater than 150 centimeters and one side is given as 45 cm, we use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
In this case, we are given that one side (length or width) of the rectangle is 45 cm. To ensure that the perimeter does not exceed 150 cm, we set up the inequality: 2(45) + 2x ≤ 150.
Simplifying the inequality gives us: 90 + 2x ≤ 150. Subtracting 90 from both sides of the inequality gives us: 2x ≤ 60.
Finally, dividing both sides by 2 to solve for x gives us: x ≤ 30. Therefore, the value of x must be less than or equal to 30 centimeters.