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 area of an older 35-inch television whose screen has an aspect ratio of 4:3

Answer 1

Greetings from Brasil...

The TV format is 4:3.

4 ÷ 3 = 1.33...

Let's assign the smallest side of the TV screen as X. Since the ratio between the sides is 4:3 = 1.33, then the other side (the largest) will be 1.33 times larger than the smaller side X, that is

smaller side = X

bigger side = 1.33X

The diagonal expression of the rectangle is:

D = √(base² + height²)

35" = √[(1.33X)² + X²]

35" = √(1.7689X² + X²) squaring both members

(35")² = 1.7689X² + X²

1225" = 2.7689X²

X² = 1225/2.7689

X² = 442.414

X = √442.414

X ≅ 21"

Tthe bigger side:

1.33X

1.33 · 21 ≅ 28"

Rectangle Area = base × height

Rectangle Area = 28 × 21

Rectangle Area = 588