Question

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 and area of the television?

Answer 1

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)`