Question

This TV has an aspect ratio of 4:3. Determine the height and width of the TV if the diagonal is 27.5.

a. Height = 18.333, Width = 24.444
b. Height = 16, Width = 22.67
c. Height = 15, Width = 20
d. Height = 12.75, Width = 17

Answer 1

The correct height of the TV with a 4:3 aspect ratio and 27.5-inch diagonal is 16.5 inches, and the width is 22 inches. None of the provided options match these values.

Step-by-step explanation:

To determine the height and width of the TV with an aspect ratio of 4:3 and a diagonal of 27.5 inches, we can use the Pythagorean theorem. Let's denote the height as H and the width as W. Since the aspect ratio is 4:3, we can write the following relation:

H/W = 3/4

This means that the height is (3/4) times the width. Let's call the width 4x and the height 3x, where x is the unit for the sides. By the Pythagorean theorem:

H² + W² = Diagonal²

(3x)² + (4x)² = (27.5)²

9x² + 16x² = 756.25

25x² = 756.25

x² = 30.25

x = √30.25

x = 5.5

Therefore, the height (H) is 3x = 3(5.5) = 16.5 inches and the width (W) is 4x = 4(5.5) = 22 inches.

None of the options provided exactly match the correct values, so the correct height is 16.5 inches and the width is 22 inches.