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A "wide-screen" TV has an aspect ratio of 16:9. Find the length of a diagonal on a...

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happyface23 | Student, Grade 10 | eNoter

Posted November 29, 2010 at 6:22 AM via web

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A "wide-screen" TV has an aspect ratio of 16:9. Find the length of a diagonal on a wide-screen TV screen that has a height of 25.2

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted November 29, 2010 at 6:27 AM (Answer #1)

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Given the wide screen TV has the ration 16/9.

Then the ration for the length to the width = 16/9.

Let L be the length and W be the width.

==> L / w = 16/ 9.

But given the width = 25.2.

Then we will substitute. 

==>  L / 25.2  = 16/9.

Now we will cross multiply.

==.> L = 25.2*16/9

            = 44.8

==> L = 44.8.

Now that we determine the width and the length of the TV, we will calculate the diagonal.

 Then, D = sqrt( L^2 + w^2)

             = sqrt( 44.8)^2 + ( 25.2)^2

             = 51.40

Then the diagonal is 51.40

 

 

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neela | High School Teacher | Valedictorian

Posted November 29, 2010 at 2:58 PM (Answer #2)

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The aspect ratio of the TV screen= 16:9.

So width : height = 16:9.

The actual height of the screen  h = 25..

Therefore  16:9 = width : height

Therefore 16:9 = x: 25.2, where x is the width .

Therefore 9x = 16*25.2.

Therefore width = x= 16*25.2/9 = 44.8.

Therefore , the diagonal =  sqrt(width^2+height^2).

diagonal = sqrt(44.8^2+25.2^2) = 51.4

So the diagonal of the TV screen = 51.4.

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