Final answer:
To find the largest possible perimeter for a rectangular poster with an area of 4500 cm² and integer dimensions, we can factorize 4500 and find all possible pairs of length and width. Calculating the perimeter for each pair, we find that the largest possible perimeter is 4504 cm.
Step-by-step explanation:
To find the largest possible perimeter Dwayne can achieve for his rectangular poster with an area of 4500 cm², let's start by finding all the possible integer dimensions that would result in an area of 4500 cm². We can factorize 4500 to find its prime factors: 4500 = 2 × 2 × 3 × 3 × 5 × 5 × 5. Since Dwayne wants the dimensions to be integers, the possible pairs of length and width could be (2, 2250), (4, 1125), (6, 750), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), (60, 75), (75, 60), (90, 50), (100, 45), (125, 36), (150, 30), (180, 25), (225, 20), (250, 18), (300, 15), (375, 12), (450, 10), (750, 6), (1125, 4), (2250, 2).
Now, let's calculate the perimeters for each pair of dimensions and find the largest one. The perimeter of a rectangle is given by P = 2(length + width). For example, for the dimensions (2, 2250), the perimeter would be P = 2(2 + 2250) = 2(2252) = 4504. By calculating the perimeters for each pair of dimensions, we find that the largest perimeter Dwayne can achieve while meeting the criteria is 4504 cm.