A television screen measures 32 inches diagonally, and its aspect ratio is 4 to 3. Find the width and the height of the screen. (Round your answers to one decimal place.)

let the length be 4x and the width 3x

then (4x)^2 + (3x)^2 = 32^2
25x^2 = 32^2
5x = 32
x = 32/5

length is 4x = 128/5 = 25.6
width is 3x = 96/5 = 19.2

To find the width and height of the screen, we can use the Pythagorean theorem and the information given.

The aspect ratio of 4 to 3 means that the width of the screen is divided into 4 equal parts and the height is divided into 3 equal parts.

Let's assume the width of the screen is 4x and the height is 3x. According to the Pythagorean theorem, the diagonal can be calculated using the formula:

diagonal^2 = width^2 + height^2

Substituting the values:

32^2 = (4x)^2 + (3x)^2
1024 = 16x^2 + 9x^2
1024 = 25x^2

Dividing by 25:

40.96 = x^2

Taking the square root of both sides, we get:

x ≈ 6.4 inches

Now, we can find the width and height of the screen:

Width = 4x = 4 * 6.4 ≈ 25.6 inches
Height = 3x = 3 * 6.4 ≈ 19.2 inches

Therefore, the width of the screen is approximately 25.6 inches and the height is approximately 19.2 inches.

To find the width and height of the screen, we can use the Pythagorean theorem.

Let's consider the width as 4x and the height as 3x (since the aspect ratio is 4 to 3).

Using the Pythagorean theorem, we have:

(width)^2 + (height)^2 = (diagonal)^2

(4x)^2 + (3x)^2 = 32^2

16x^2 + 9x^2 = 1024

25x^2 = 1024

x^2 = 1024/25

x^2 = 40.96

x ≈ √40.96

x ≈ 6.4

Now we can find the width and height:

Width = 4x ≈ 4 * 6.4 = 25.6 inches

Height = 3x ≈ 3 * 6.4 = 19.2 inches

Therefore, the width of the screen is approximately 25.6 inches, and the height is approximately 19.2 inches.