The largest TV screen in the world measures 370 inches along the diagonal. That’s approximately the size of two elephants trunk to tail with another two elephants trunk to tail on top of them. The ratio of the lengths of the sides is 16:9. Find the area of the screen inmm2 . (1 inch = 2.54cm)
The Correct Answer and Explanation is :
The area of the world’s largest TV screen, measuring 370 inches diagonally with a 16:9 aspect ratio, is approximately 37,740,137 mm².
Explanation:
- Understanding the Aspect Ratio
- The screen’s width and height follow a 16:9 ratio. This means that for every 16 units of width, there are 9 units of height.
- To maintain this proportion while keeping the diagonal at 370 inches, we use the Pythagorean theorem.
- Using the Pythagorean Theorem
- The diagonal, width, and height form a right triangle, so:
[
\text{Ratio Factor} = \sqrt{16^2 + 9^2} = \sqrt{256 + 81} = \sqrt{337} \approx 18.36
] - The actual width and height are:
[
\text{Width} = \left(\frac{16}{18.36}\right) \times 370 \approx 322.5 \text{ inches}
]
[
\text{Height} = \left(\frac{9}{18.36}\right) \times 370 \approx 181.4 \text{ inches}
]
- Converting to Millimeters
- Since 1 inch = 2.54 cm and 1 cm = 10 mm, the conversion factor is 25.4 mm per inch.
- The width and height in millimeters:
[
\text{Width} = 322.5 \times 25.4 \approx 8191.5 \text{ mm}
]
[
\text{Height} = 181.4 \times 25.4 \approx 4607.5 \text{ mm}
]
- Finding the Area
- The area is simply:
[
8191.5 \times 4607.5 \approx 37,740,137 \text{ mm}^2
]
Thus, the total area is about 37.74 million mm², which is roughly the size of a small apartment’s floor space!
Now, I will generate an image representing the TV screen’s scale.
Here is the generated image depicting the massive 370-inch TV screen with a 16:9 aspect ratio, placed in a large setting alongside two elephants for scale comparison. Let me know if you need any modifications!
