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Determine the dimensions of the screen of a 42-inch TV with a 4:3 aspect ratio. (Hint: Use (3x)^2+(4x)^2=42^2 to help you find the dimensions).

 Sep 3, 2019
edited by Guest  Sep 3, 2019
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It is a 42-inch TV. This means the length of the diagonal is 42 inches.

 

Aspect ratio is the ratio of the width to the height.

So if we let the unknown scale factor be called  s ,

then  the width  =  4s

and  the height  =  3s

 

 

Now we can use the Pythagorean Theorem to find what  s  is.

 

(4s)2 + (3s)2  =  422    This is the equation given in the hint.

 

(4s)(4s) + (3s)(3s)  =  422

 

16s2 + 9s2  =  422

                                   Just like  16 apples + 9 apples = 25 apples, so does  16s2 + 9s2 = 25s2

25s2  =  422

                       Let's rewrite  25s2  like this...

(5s)2  =  422

                       and take the square root of both sides.

5s  =  42

 

s  =  8.4    (inches)

 

Now that we know what  s  is, we can find the width and the height.

width  =  4s  =  4(8.4)  =  33.6    (inches)

height  =  3s  =  3(8.4)  =  25.2    (inches)

 Sep 3, 2019

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