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

Part 1) The area of a 17 in traditional tv screen is
`A=138.7\ in^2`

Part 2) The area of a 17 in LCD TV screen is
`A=123.5\ in^2`

Part 3) The screen of the 17 in traditional TV is bigger, because its area is greater than the area of the LCD TV

Explanation:

Let

x ----> the length of the rectangular screen

y ----> the width of the rectangular screen

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

we have

`(x)/(y)=(4)/(3)`

`x=(4)/(3)y` ----> equation A

Applying the Pythagorean Theorem

`x^(2) +y^(2) =17^(2)` ----> equation B

substitute equation A in equation B

`((4)/(3)y)^(2) +y^(2) =17^(2)`

solve for y

`(16)/(9)y^(2) +y^(2) =289`

`(25)/(9)y^(2)=289`

take square root both sides

`(5)/(3)y=17`

`y=17(3)/5\\y=10.2\ in`

Find the value of x

`x=(4)/(3)(10.2)`

`x=13.6\ in`

Find the area of the rectangular screen

The area is equal to

`A=xy`

substitute

`A=(13.6)(10.2)=138.72\ in^2`

`A=138.7\ in^2`

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

we have

`(x)/(y)=(16)/(9)`

`x=(16)/(9)y` ----> equation A

Applying the Pythagorean Theorem

`x^(2) +y^(2) =17^(2)` ----> equation B

substitute equation A in equation B

`((16)/(9)y)^(2) +y^(2) =17^(2)`

solve for y

`(256)/(81)y^(2) +y^(2) =289`

`(337)/(81)y^(2)=289`

take square root both sides

`(√(337))/(9)y=17`

`y=17(9)/√(337)`

`y=(153)/(√(337))\ in`

Find the value of x

`x=(16)/(9)((153)/(√(337)))`

`x=(2,448)/(9√(337))\ in`

Find the area of the rectangular screen

The area is equal to

`A=((2,448)/(9√(337)))((153)/(√(337)))`

`A=123.49\ in^2`

`A=123.5\ in^2`

Part 3) which screen is bigger?

Compare the areas

`138.7\ in^2 > 123.5\ in^2`

therefore

The screen of the 17 in traditional TV is bigger, because its area is greater than the area of the LCD TV