Final answer:
The percent occupation of the monitor's area by the video image was mistakenly calculated as 180%, which exceeds the physical limit. Letter-boxing suggests the image is scaled down, implying a reevaluation of calculations or question premise is required.
Step-by-step explanation:
To find the percent of the screen's area occupied by the image, first, we need to understand that the monitor's aspect ratio of 4:3 and the video image's ratio of 24:10 represent their width and height respectively.
Let's express both ratios with the same height to find the relative width of the video image on the monitor:
- The monitor's aspect ratio is 4:3. If we take the height as 3, the width would be 4.
- The video's aspect ratio is 24:10. We can simplify this to 12:5 to make calculations easier. To scale the video's height to the monitor's height, we multiply the height by 3/5, resulting in 3 (they now have the same height). The width also needs to be multiplied by 3/5, resulting in a width of 7.2 for the video image.
Now we have the scaled width of the video as 7.2 with a height of 3, compared to the monitor's width of 4 with the same height. Since the length units are arbitrary, we don't need the actual lengths to calculate the area percentage.
The monitor's area is:
Monitor Area = width x height = 4 x 3 = 12
The video's area on the monitor is:
Video Area = width x height = 7.2 x 3 = 21.6
Finally, calculate the percentage of the screen's area occupied by the image:
Percent Occupied = (Video Area / Monitor Area) x 100 = (21.6 / 12) x 100 = 180%
However, since the image cannot exceed the screen's area, the maximum occupation is 100%. Thus, there is a misunderstanding, as the video image cannot physically occupy 180% of the monitor's space. If letterboxing is present, this implies that the video is being scaled down to fit within the monitor's aspect ratio. We might need to reconsider our calculations or the premise of the question.