Question

The screen size of a television is determined by the length of the diagonal of the rectangular screen. traditional elevisions come in a 4:3 format, meaning the ratio of the length to width of the screen is 4 to 3
What is the area of a 17in traditional tv screen? What is the area of a 17in LCD TV whose screen is in 16:9 format? which screen is bigger?

The area of a 17 inch traditional tv is approximately _______ sq inches

LCD is________ " "
(Do not round until the final answer. Then round one decimal place as needed)​

Answer 1

Answer:

• The area of a 17 in traditional TV is approximately 138.7 in².

• The area of a 17 in LCD TV is approximately 123.3 in²

• The 17 in LCD TV's screen is bigger

Explanation:

1. What is the area of a 17in traditional tv screen?

a) Measure of the diagonal = 17 in

b) The diagonal is the hypotenuse of a triangle.

c) Call x and y the length and the width of the screen. Then, by Pythagora's theorem:

• x² + y² = 17²

d) Since the ratio of the length to the width of the screen is 4:3

• x/y = 4/3

e) Solve the system of equations:

• x = 4y/3

• (4y/3)² + y² = 17²

• 16y²/9 + y² = 17²

• 16y² + 9y² = 17² × 9

• 25y² = 17² × 9

• y² = 17² × 9 / 25

• y = 17 × 3 / 5 = 10.2 in

• x = 10.2 × 4 / 3 = 13.6 in

f) Area = x × y = 10.2 in × 13.6 in = 138.72 in²

The area of a 17 inch traditional TV is approximately 138.7 in²

2. What is the area of a 17in LCD TV whose screen is in 16:9 format?

• x² + y² = 17²

• x/y = 16/9

Solve the system of equations:

• x = 16y/9

• (16y/9)² + y² = 17²

• 256y²/81 + y² = 17²

• 256y² + 81y² = 17² × 81

• 337y² = 17² × 81

• y² = 17² × 81 / 337

• y = = 8.33 in

• x = 8.33 × 16 / 9 = 14.8 in

Area = x × y = 14.8 in × 8.33 in = 123.28 in²

The area of a 17 inch LCD TV is approximately 123.3 in²

3. Which screen is bigger?

The screen of the 17 in traditional TV is bigger, because its area (approximately 138.7 in²) is greater than the area of the LCD TV (approximatle 123.3 in²).