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TV has a diagonal length of 42in. (For the viewing area), // Modern Tv s have a ratio of 16:9 for the width:height.?
How wide and how high is the viewing area of this TV?
The answer in the back of the book is
36.61"wide 20.59" height
But I'm not sure how to get there... any help would be greatly appreciated.
1 Answer
- PuzzlingLv 72 years agoFavorite Answer
The aspect ratio is 16:9 which means that it is 16 units wide for every 9 units tall.
We can write that as follows:
Let 16x be the width
Let 9x be the height
Using the Pythagorean Theorem:
(16x)² + (9x)² = 42²
Expand:
256x² + 81x² = 1764
Combine like terms:
337x² = 1764
x² = 1764/337
x = √(1764/337) <-- technically there are two possible roots (positive and negative) but since we are dealing with dimensions, we only care about the positive root.
x ≈ 2.288
Now we can figure out the two dimensions:
Width (16x) --> 16 * 2.288 ≈ 36.61" wide
Height (9x) -->: 9 * 2.288 ≈ 20.59" tall
