Final answer:
The greatest possible perimeter for Dwayne's rectangular poster with the area of 4500 cm², with integer length and width, is just below 280 cm, which is the nearest option to twice the side of a square with the given area (approximately 2 × 67 cm = 2 × 67 cm = 268 cm). Therefore, option (A) 280 cm is the correct choice.
Step-by-step explanation:
The question posed is a geometry problem, where we need to determine the greatest possible perimeter of a rectangle with a given area, with the condition that the dimensions must be integers. Since the area of the rectangle is 4500 cm2, we need to find two factors of 4500 that are integers and their sum would give us half of the perimeter (since a perimeter of a rectangle is calculated by adding twice the length and twice the width).
By analyzing the options given, we can see that (B) 4504 cm and (C) 9002 cm are too large to be feasible perimeters for an area of 4500 cm2, since even a square, which has the smallest perimeter for a given area, of side length √4500 cm is far less than those options in perimeter. Option (D) 18000 cm is simply too large to consider. So we're left with option (A) which is plausible. The maximum perimeter of a rectangle is when it's a square, here √4500 cm ≈ 67 cm (rounded to nearest integer), so the greatest perimeter with integer dimensions will be 2(l + w) = 2(67 + 67) = 268 cm, which is close to option (A) 280 cm. Hence, the greatest integer-dimension perimeter of the poster is likely just below 280 cm.