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Thread: measurents of TV

  1. #1
    ttG
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    measurents of TV

    A STANDARD picture format TV has a screen where the width is 4/3 of the height.
    A WIDESCREEN TV has a screen where the width is 16/9 of the height.
    Consider 2 TVs that are the same size, which means that the diagonals(28 inches= 2.54cm) of the screens are the same length, but where one of them is of the standard pic format and the other one- widescreen.

    Determine screen wil have the largest area.
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  2. #2
    Member Danshader's Avatar
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    considering th standard one first:

    given that the width is 4/3 of the height

    height, h = h
    width, w =$\displaystyle \frac{4}{3}h$

    also given that that size of the TV is 28 inches(71.12 cm), this is actually the hypotenuse of the TV

    $\displaystyle
    28^2 = h^2 + w^2
    $

    $\displaystyle
    28^2 = h^2 + {(\frac{4}{3}h)}^2
    $

    $\displaystyle
    784 = h^2 + \frac{16}{9}h^2
    $

    $\displaystyle
    784 = \frac{25}{9}h^2
    $

    $\displaystyle
    h^2 = 282.24 inches
    $

    $\displaystyle
    h = 16.8 inches
    $

    Area of the screen
    = area of a rectangle with a diagonal of 28 inches
    $\displaystyle
    =width \times height
    $
    $\displaystyle
    =\frac{4}{3}h\cdot h
    $
    $\displaystyle
    =\frac{4}{3} h^2
    $
    $\displaystyle
    = \frac{4}{3} (282.24)
    $
    $\displaystyle
    = 376.32 inches^2
    $

    do the same thing for the widescreen TV and i get 335.003 inches^2. Hence concluding that the standard picture TV has a larger area.
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  3. #3
    ttG
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    Thank u!
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