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Math Help - TV

  1. #1
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    TV

    A television screen is 40 cm high and 60 cm wide. The picture is compressed to 62.5 % of its original area, leaving a uniform dark strip around the outside. What are the dimensions of the reduced picture?
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  2. #2
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    Would it not be 30cm by 50cm?
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  3. #3
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    Hello, Andrew!

    A television screen is 40 cm high and 60 cm wide.
    The picture is compressed to 62.5 % of its original area,
    leaving a uniform dark strip around the outside.
    What are the dimensions of the reduced picture?
    Let x = width of the dark strip.
    Code:
          : - - -  60 - - - - :
        - *-------------------* -
        : |                   | x
        : |   *-----------*   | -
        : |   |           |   | : 
       40 |   |           |   | 40-2x
        : |   |           |   | :
        : |   *-----------*   | -
        : |                   | x
        - *-------------------* -
          : x :   60-2x   : x :
    The area of the screen is: . 40 \times 60 \:=\:2400 cm².

    The area of the picture is: . (40-2x)(60-2x) \:=\:4x^2 - 200x + 2400 cm².


    The area of the picture is \frac{5}{8} the area of the screen:

    . . 4x^2 - 200x + 2400 \:=\:\frac{5}{8}(2400) \;=\;1500 \quad\Rightarrow\quad 4x^2 - 200x + 900 \:=\:0

    Factor: . 4(x-5)(x-45) \:=\:0 \quad\Rightarrow\quad x \;=\;5,\:45

    The dark strip is 5 cm wide.


    Therefore, the dimensions of the picture are: . 30\text{ cm } \times 50\text{ cm.}


    You're absolutely correct, Lucky!

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