Your mother wants to get a new television but she would like to have an older model with an aspect ratio of 4:3 she is looking at a 32 inch television. what is the width height …

Question

asked Jul 11, 2020 191k views

1 Answer

Chris Morgan · Answer 1 · 2020-07-14T22:49:34+0000

Answer:

Part A) The height of the television is
$25.6\ in$

Part B) The width of the television is
$19.2\ in$

Part C) The area of the television is
$491.52\ in^(2)$

Explanation:

Let

x-----> the width of the television

y-----> the height of the television

we know that

The diagonal of the television is
$32\ in$

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

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

Applying the Pythagoras Theorem

${y^(2) +x^(2)} =32^(2)$ ------> equation B

substitute the equation A in equation B

${((4)/(3)x)^(2) +x^(2)} =32^(2)$

${(16)/(9)x^(2) +x^(2)} =1,024$

${(25)/(9)x^(2)=1,024$

$x=3*32/5=19.2\ in$

Find the value of y

y=(4)/(3)x ------->
$y=(4)/(3)(19.2)=25.6\ in$

Find the area of the television

The area of rectangle is equal to

A=bh

substitute

$A=19.2*25.6=491.52\ in^(2)$