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:

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

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

$\frac{x}{y}=\frac{4}{3}$

$x=\frac{4}{3}y$ ----> equation A

Applying the Pythagorean Theorem

$x^{2} +y^{2} =17^{2}$ ----> equation B

substitute equation A in equation B

$(\frac{4}{3}y)^{2} +y^{2} =17^{2}$

solve for y

$\frac{16}{9}y^{2} +y^{2} =289$

$\frac{25}{9}y^{2}=289$

take square root both sides

$\frac{5}{3}y=17$

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

Find the value of x

$x=\frac{4}{3}(10.2)$

$x=13.6\ in$

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

$\frac{x}{y}=\frac{16}{9}$

$x=\frac{16}{9}y$ ----> equation A

Applying the Pythagorean Theorem

$x^{2} +y^{2} =17^{2}$ ----> equation B

substitute equation A in equation B

$(\frac{16}{9}y)^{2} +y^{2} =17^{2}$

solve for y

$\frac{256}{81}y^{2} +y^{2} =289$

$\frac{337}{81}y^{2}=289$

take square root both sides

$\frac{\sqrt{337}}{9}y=17$

$y=17(9)/\sqrt{337}$

$y=\frac{153}{\sqrt{337}}\ in$

Find the value of x

$x=\frac{16}{9}(\frac{153}{\sqrt{337}})$

$x=\frac{2,448}{9\sqrt{337}}\ in$

Find the area of the rectangular screen

The area is equal to

$A=(\frac{2,448}{9\sqrt{337}})(\frac{153}{\sqrt{337}})$

$A=123.49\ in^2$

$A=123.5\ in^2$

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