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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)​

Respuesta :

calculista

Answer:

Part 1) The area of a 17 in traditional tv screen is [tex]A=138.7\ in^2[/tex]

Part 2) The area of a 17 in LCD TV screen is [tex]A=123.5\ in^2[/tex]

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

Step-by-step 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

[tex]\frac{x}{y}=\frac{4}{3}[/tex]

[tex]x=\frac{4}{3}y[/tex] ----> equation A

Applying the Pythagorean Theorem

[tex]x^{2} +y^{2} =17^{2}[/tex] ----> equation B

substitute equation A in equation B

[tex](\frac{4}{3}y)^{2} +y^{2} =17^{2}[/tex]

solve for y

[tex]\frac{16}{9}y^{2} +y^{2} =289[/tex]

[tex]\frac{25}{9}y^{2}=289[/tex]

take square root both sides

[tex]\frac{5}{3}y=17[/tex]

[tex]y=17(3)/5\\y=10.2\ in[/tex]

Find the value of x

[tex]x=\frac{4}{3}(10.2)[/tex]

[tex]x=13.6\ in[/tex]

Find the area of the rectangular screen

The area is equal to

[tex]A=xy[/tex]

substitute

[tex]A=(13.6)(10.2)=138.72\ in^2[/tex]

[tex]A=138.7\ in^2[/tex]

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

we have

[tex]\frac{x}{y}=\frac{16}{9}[/tex]

[tex]x=\frac{16}{9}y[/tex] ----> equation A

Applying the Pythagorean Theorem

[tex]x^{2} +y^{2} =17^{2}[/tex] ----> equation B

substitute equation A in equation B

[tex](\frac{16}{9}y)^{2} +y^{2} =17^{2}[/tex]

solve for y

[tex]\frac{256}{81}y^{2} +y^{2} =289[/tex]

[tex]\frac{337}{81}y^{2}=289[/tex]

take square root both sides

[tex]\frac{\sqrt{337}}{9}y=17[/tex]

[tex]y=17(9)/\sqrt{337}[/tex]

[tex]y=\frac{153}{\sqrt{337}}\ in[/tex]

Find the value of x

[tex]x=\frac{16}{9}(\frac{153}{\sqrt{337}})[/tex]

[tex]x=\frac{2,448}{9\sqrt{337}}\ in[/tex]

Find the area of the rectangular screen

The area is equal to

[tex]A=(\frac{2,448}{9\sqrt{337}})(\frac{153}{\sqrt{337}})[/tex]

[tex]A=123.49\ in^2[/tex]

[tex]A=123.5\ in^2[/tex]

Part 3) which screen is bigger?

Compare the areas

[tex]138.7\ in^2 > 123.5\ in^2[/tex]

therefore

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

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