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Math Help - Areas

  1. #1
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    Areas

    A 5x5 square and a 3x3 square can be cut into pieces that will fit together to form a third square.
    a. find the length of a side of the 3rd square
    b. in the diagram mark P on the segment DC so that PD = 3, then draw the segments PA and PF. Calculate the lengths of these segments.
    c. segments PA and PF divide the squares into pieces. Arrange the pieces to form the third square.
    ^what?! i dont get this
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  2. #2
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    Quote Originally Posted by gabriel View Post
    A 5x5 square and a 3x3 square can be cut into pieces that will fit together to form a third square.
    a. find the length of a side of the 3rd square

    how large is the side of a square that is made from 5x5 + 3x3 = 25 + 9 = 34 square units?

    b. in the diagram mark P on the segment DC so that PD = 3, then draw the segments PA and PF. Calculate the lengths of these segments.
    c. segments PA and PF divide the squares into pieces. Arrange the pieces to form the third square.
    ^what?! i dont get this

    neither do I ... what diagram?
    ...
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  3. #3
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    this is the diagram

    segment AB is unknown
    segment AD = 5 units
    segment DC= 5 units
    segment BC is unknown
    ^square 1
    segment GF is unknown
    segment CE= 3 units
    segment FE= 3 units
    segment GC is unknown
    ^square 2
    *square 2 is adjacent to sqaure 1
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  4. #4
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    Hello, gabriel!

    Your description is quite confusing.
    I'll take a guess at what the diagram looks like.


    \text{A }5\times5\text{ square and a }3\times3\text{ square can be cut into pieces}
    . . . \text{that will fit together to form a third square.}

    \text{(a) Find the length of a side of the 3rd square.}

    \text{(b) In the diagram mark }P\text{ on the segment }DC\text{ so that }PD = 3.
    . . . \text{Then draw the segments }PA\text{ and }PF.
    . . . \text{Calculate the lengths of these segments.}

    \text{(c) Segments }PA\text{ and }PF\text{ divide the squares into pieces.}
    . . . \text{Arrange the pieces to form the third square.}

    The area of the large square is: . 5^2 = 25 square units.
    The area of the small square is: . 3^2 = 9 square units.
    . . The area of the third square is: . 25 + 9 \:=\:34 square units.

    Therefore, the side of the third square is \sqrt{34} units.



    I would guess that the diagram looks like this:


    Code:
                    5
        A o - - - - - - - - - o B
          |*                  |
          | *                 |
          |  *                |
          |   *               |
          |    *              |    3 
        5 |     *           G o - - - - o F
          |      *            |      *  |
          |   P   *           |   *     |
          |        *          |*        | 3
          |         *       * |    R    |
          |          *   *  Q |         |
          o - - - - - o - - - o - - - - o
          D     3     P   2   C    3    E

    PA and PF are hypotenuses of right triangles with legs 3 and 5.

    Hence, theire lengths are: . \sqrt{3^2+5^2} \:=\:\sqrt{34}




    Move the pieces labeled P,Q,R to their new locations.


    Code:
                              *
                            * |*
                         *    | * 
                      *       |  *
                   *          |   *
                *  |     R    |    *
             *  Q  |          |     *
        A o--------*----------o      *
          .*                  |   P   *
          . *                 |        *
          .  *                |         *
          .   *               |          *
          .    *            G o-----------o F
          .     *             |         * .
          .      *            |      *    .
          .       *           |   *       .
          .        *          |*          .
          .         *       * .           .
          .          *   *    .           .
          . . . . . . o . . . . . . . . . .
                      P
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