{ 3 \frac{1}{2} in. \times 5 in }. photograph is enlarged to a 28 in. { \times } 40 in....

Question:

{eq}3 \frac{1}{2} in. \times 5 in {/eq}. photograph is enlarged to a 28 in. {eq}\times {/eq} 40 in. poster. What is the scale of the poster?

Photograph Scale Factor

The idea of the scale factor is extensively used in photo enlargement. In early times, cameras used films to capture images. These were developed to any larger images with the same aspect ratio as the film. This was also applied nowadays in digital cameras, wherein the images can be enlarged by any scale factor while maintaining its aspect ratio.

Answer and Explanation:

The scale factor is given by

{eq}SF=\dfrac{final\,width}{original\,width}=\dfrac{final\,length}{original\,length}\\ {/eq} Note that this is only true if the aspect ratio of the image is maintained. Thus,

{eq}SF=\dfrac{28\,in.}{3 \frac{1}{2}\,in.}=\dfrac{40\,in.}{5\,in.}\\[0.2cm] \mathbf{SF=8}\\[0.2cm] {/eq} Therefore, the scale of the poster is 8:1.


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