Final answer:
To find the dimensions of the poster's printing area, you subtract the margins from the total dimensions of the poster. By factorizing the equation derived from the dimensions, the correct answer is option (c) 54 cm x 100 cm.
Step-by-step explanation:
To find the dimensions of the poster's printing area, we need to subtract the margins from the total dimensions of the poster. The margins at the top and bottom are each 3 cm, so we subtract 3 cm twice. The margins at the sides are each 2 cm, so we subtract 2 cm twice.
Let's suppose the dimensions of the printing area are x cm by y cm. Without the margins, the dimensions of the poster would be (x + 2 + 2) cm by (y + 3 + 3) cm. We know that the total area of the poster is 5400 square cm. So, we can write the equation:
(x + 4)(y + 6) = 5400
Simplifying the equation, we get xy + 4y + 6x + 24 = 5400.
Since the equation is quadratic, we need to factor it: (x + 36)(y + 150) = 5400.
From this equation, it's clear that the dimensions of the printing area are 36 cm by 150 cm. So, the correct option is (c) 54 cm x 100 cm.