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Thread: Word Problem for Linear-Quadratic Systems

  1. #1
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    Word Problem for Linear-Quadratic Systems

    A square cupboard door contains four square panels. The border around each square panel has a uniform width of 4 cm. if the total area of the door excluding the panels is 720 cm^2, what are the dimensions of the door and each panel.

    use substitution

  2. #2
    Elite Member stapel's Avatar
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    How far have you gotten? You've drawn the picture and... then what?

    Please reply with specifics. Thank you.

    Eliz.

  3. #3
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    well the picture looks something like this:



    and then i was thinking that one of the equations was x^2=720. but i think thats wrong. and i havent figured out the second one yet. cause i made the boxes inside equal to y and if each border was 4 cm i was thinking it would be 16...

  4. #4
    Elite Member stapel's Avatar
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    What does "x" stand for? Or "y"?

    Please include units in your description. Thank you.

    Eliz.

  5. #5
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    oh yeah. i put my X= to one of the sides on the big square. and my Y=to one of the sides in the smaller square.

  6. #6
    Elite Member stapel's Avatar
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    Thank you for the clarification (and my apologies for the delay in my reply, but I only just now got back home).

    If the length of the side of an interior (and square) panel is "y", then the area of one panel is y<sup>2</sup> and the area of all four panels is 4y<sup>2</sup>.

    Looking at the graph, the width of the door is 4 + y + 4 + y + 4 = 2y + 12. So is the height. So what is the area?

    Now subtract the panel area from the total area, set equal to the given "door less panels" area, and solve.

    I don't know what they mean by "use substitution". Sorry.

    Eliz.

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