Final answer:
The area of a 27-inch 4:3 aspect ratio TV screen is 349.92 square inches when rounded to two decimal places. This is calculated by determining the width and height that correspond to the aspect ratio and then using the Pythagorean theorem to solve for the scaling factor given the diagonal size.
Step-by-step explanation:
To calculate the area of the screen of a 27-inch 4:3 aspect ratio TV, we need to find the dimensions of the screen that correspond to the diagonal size. The aspect ratio 4:3 represents the ratio of the width to the height of the screen. We can set up a right-angled triangle with the 27-inch diagonal as the hypotenuse, the width as 4x, and the height as 3x, where x is a scaling factor.
We use the Pythagorean theorem to solve for x:
4x^2 + 3x^2 = 27^2
16x^2 + 9x^2 = 729
25x^2 = 729
x^2 = 729/25
x = sqrt(729/25)
x = 27/5
Now, we can find the actual width and height:
Width = 4x = 4(27/5) = 21.6 inches
Height = 3x = 3(27/5) = 16.2 inches
To get the area, multiply the width and height:
Area = Width x Height
Area = 21.6 inches x 16.2 inches = 349.92 square inches
Rounded to two decimal places, the area is 349.92 square inches.