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How to calculate the maximum height or width of an image based on the canvas size or poster card size? example: image size is as below:

height: 3648,
width: 5472, and 
poster card size: 150 * 100 (W*H) 

if i request for width 80 what can be the max height based on the image dimensions and poster card size

so what can be the max width or height? please guide me

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150 cm / 100 cm = (50 * 3) / (50 * 2) = 3 / 2
 80 cm / 2 * 3  = 120 cm

As you do not have to crop, you could still use the full resolution of the picture. However, the resolution (PPI - pixels per inch) changes: The smaller the canvas, the higher the PPI can be.

For a better understanding of PPI, canvas sizes, picture resolutions, and how those terms are connected, you can read through these questions and their answers:

1As mentioned by @Zenit in a comment.

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Your image has an aspect ratio of 3:2, so does your poster card.
That means that the width of your image and poster card is 1.5× the height.

So for a card width of 80 and an image width of 5472,
your image height should be 3648.

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If we know the height and width of an image, we can calculate the ratio of height to width by simple division. This math determines the “aspect ratio” of the image. Thus 5472 ÷ 3648 = 1.5. Now we know the aspect ratio is 1.5. This tells us that if we wish to print this image on paper, and we don’t wish to crop the image, the paper size must also have a ratio of 1.5. The good news is, a ratio works regardless of the unit of measure. As an example, if the height of the paper is 4 inches, the length will be 4 X 1.5 = 6 inches. If the paper is to be 80 centimeters in height, the length must be 80 X 1.5 = 120 centimeters length. Again, the beauty of an aspect ratio is that it is void of unit of measure; thus it works for all the units. One more example, a giant poster 22 yards high will be 22 X 1.5 = 33 yards long.

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