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Math Help - [SOLVED] Finding areas

  1. #1
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    [SOLVED] Finding areas

    Hi I need some more help with word problems. I don't know if I can get some help because there are drawings that go with it but I'll explain them as best as I can. Or maybe just some ideas on how to plug it into an equation.

    1. Length and area. Find the length y in the figure. The area of the shaded region is given. both pictures are completely shaded. There is an attached picture.
    Attached Thumbnails Attached Thumbnails [SOLVED] Finding areas-word-prob.bmp  
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  2. #2
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    Hello, Lucy!

    Are you sure that you couldn't figure these out yourself?


    Find the length y in the figure.
    Code:
                      * - - - - - *
                    * |           |
                  *   |           |
                *     |           | y    Area: 120 in²
              *       |           |
            *         |           |
          * - - - - - * - - - - - *
                y           y

    The triangle has area: . \tfrac{1}{2}y^2

    The square has area: . y^2

    The total area is 120 in²: . \tfrac{1}{2}y^2 + y^2 \:=\:120 \quad\Rightarrow\quad\tfrac{3}{2}y^2 \:=\:120 \quad\Rightarrow\quad y^2 \:=\:80

    Therefore: . y \:=\:\sqrt{80} \:=\:4\sqrt{5}\text{ in.}




    Code:
                      * - - *
                    * |     |
                  *   |     |
                *     |     | y    Area: 1200 cm²
              *       |     |
            *         |     |
          * - - - - - * - - *
                y        1

    The triangle has area: . \tfrac{1}{2}y^2

    The rectangle has area: . y\cdot1 \:=\:y

    The total area is 1200 cm²: . \tfrac{1}{2}y^2 + y \:=\:1200 \quad\Rightarrow\quad y^2 + 2y - 2400 \:=\:0

    . . which factors: . (y-48)(y+50) \:=\:0

    . . and has the positive root: .  y \:=\:48

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  3. #3
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    questions and thanks yous for word problem help

    Thank you so much for your help. I am extremely bad at word problems I have been working on these for the past three days and nothing came to me. I am also a little confused as to where the 2y and 2400 came from in B. Thank you again.
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