Question

The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Answer 1

Answer:

The Width = 65.44 inches

The Height = 36.81 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Using Pythagoras Theorem we known that:

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 75²

We are given ratio: 16:9 as aspect ratio

Width = 16x

Height = 9x

(16x)² +(9x)² = 75²

= 256x² + 81x² = 75²

337x² = 5625

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately x = 4.09

For the newer 75 inch tv set

The Height = 9x

= 9 × 4.09

= 36.81 inches

The Width = 16x

= 16 × 4.09

= 65.44 inches.