Answer:
The area is approximately 1240.17 square inches.
Explanation:
The aspect ratio of 4:3 means that for every 4 units of width, there are 3 units of height. Let's use "w" to represent the width of the screen, and "h" to represent the height.
We know that the ratio of width to height is 4:3, so we can write:
w:h = 4:3
To solve for the width and height, we can use cross-multiplication:
w/h = 4/3
Multiplying both sides by "h" gives:
w = (4/3)h
Now we need to find the values of "w" and "h". Since we're given that the screen is 50 inches diagonally, we can use the Pythagorean theorem to relate the width, height, and diagonal:
w^2 + h^2 = 50^2
Substituting w = (4/3)h:
(4/3)h^2 + h^2 = 50^2
Multiplying by 3 to eliminate the fraction:
4h^2 + 3h^2 = 3(50^2)
Simplifying:
7h^2 = 3(50^2)
h^2 = (3/7)(50^2)
Taking the square root of both sides:
h = 30.51 inches
Now we can use the equation w = (4/3)h to find the width:
w = (4/3)(30.51) = 40.68 inches
The area of the screen is simply the product of the width and height:
Area = w * h = (40.68)(30.51) = 1240.17 square inches
Therefore, the width of the screen is approximately 40.68 inches, the height is approximately 30.51 inches, and the area is approximately 1240.17 square inches.
Here is a rough sketch to help visualize the dimensions of the screen:
(Attachment)
The diagonal is the hypotenuse of a right triangle with sides of 40.68 inches and 30.51 inches. The area is the product of these two sides.
*I am not an artist* ---Down below.