To find the dimensions of the poster, we start with the information provided:
- Top and bottom margins: 9 cm each
- Side margins: 6 cm each
- Area of printed material: 864 cm²
Let the width of the poster be w cm and the height be h cm.
The printed area is determined by subtracting the margins from the total dimensions of the poster. The width of the printed area is:
Width of printed area = w – 2 * (side margins) = w – 2 * 6 = w – 12 cm
The height of the printed area is:
Height of printed area = h – 2 * (top and bottom margins) = h – 2 * 9 = h – 18 cm
Now, the area of the printed material can be expressed as:
(w – 12)(h – 18) = 864
Expanding this, we get:
wh – 18w – 12h + 216 = 864
Which simplifies to:
wh – 18w – 12h = 648
Next, we express h in terms of w:
h = (648 + 18w + 12h) / w
To find realistic dimensions, let’s assume a reasonable width. For instance, let’s try w = 48 cm:
Substituting w = 48 into the area equation:
(48 – 12)(h – 18) = 864
36(h – 18) = 864
h – 18 = 24
h = 42 cm
Therefore, when we check our dimensions:
- Width of the poster: 48 cm
- Height of the poster: 42 cm
Finally, the dimensions of the poster are:
- Width: 48 cm
- Height: 42 cm
This ensures that the area of printed material remains fixed at 864 cm² with the given margins.