Sure, let's calculate the percentage difference in viewing area between your 55 inch widescreen TV and your brother's 65 inch widescreen TV, based on the diagonal measurement.
The viewing area of a TV is calculated based on its diagonal measurement and aspect ratio. Most widescreen TVs have an aspect ratio of 16:9. Therefore, we can use the formula for the area of a rectangle, which is length times width. However, since we have the diagonal and the aspect ratio, we can use these to calculate the length and width.
Let's calculate the areas of both TVs and then find the percentage difference.
The calculation shows that your TV has approximately -28.4% more viewing area than your brother's. However, since the percentage is negative, it means that your TV actually has about 28.4% less viewing area than your brother's 65-inch TV.