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Math Help - Adding a "Perimeter" to a Shape

  1. #1
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    Adding a "Perimeter" to a Shape

    Adding a "Perimeter" to a Shape-2rele0z.png

    Assumptions
    I have a piece of fabric shaped like the blue shape and its measurements are (in inches):
    a = 25
    b = 18.384
    c = 18.384


    Problem
    The green shape represents a "perimeter" piece of fabric six inches wide that I want to attach to the blue shape. What are the measurements of x, y, and z?


    My brain hurts from trying to solve this problem over the past couple days. Thanks for your help :-)
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  2. #2
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    Hello, nkline!

    If that's all that's given, we can't solve the problem.


    \text{I have a piece of fabric (shaded region) with measurements:}

    . . a = 25,\;b = 18.384,\;c = 18.384\text{ inches.}

    \text{It is bordered on three sides with a 6-inch wide strip of fabric.}

    \text{What are the measurements of }\,x,\:y,\,\text{ and }\,z\:?

    I will assume that we have isosceles trapezoids: . b = c,\;y = z

    But, even then, there is insufficient information.


    Code:
                            x
                  D * - - - - - - - * C
                   /                 \
                  / *               * \
                 /  6 *     a     * 6  \
                /       * - - - *       \
             y /       /:::::::::\       \ y
              /       /:::::::::::\       \
             /      b/:::::::::::::\b      \
            / * 6   /:::::::::::::::\   6 * \
           /@   *  /:::::::::::::::::\  *    \
        A * - - - * - - - - - - - - - * - - - * B

    We need another piece of information:
    . . the base angle of the trapezoids \,\theta
    . . or the length of the base of the inner trapezoid.
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  3. #3
    MHF Contributor
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    Once we have the add'l information (as per Soroban), then it's easy enough;
    we have similar triangles to make our lives easier, plus we only need to work
    with one "portion" of the trapezoid (left half or right half).
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  4. #4
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    Adding a "Perimeter" to a Shape

    Thank you for the quick replies :-)

    We need another piece of information:
    . . the base angle of the trapezoids
    . . or the length of the base of the inner trapezoid.
    The length of the base of the inner trapezoid (the blue shape in my diagram) is 51 inches.
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  5. #5
    MHF Contributor
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    Is there a reason why you didn't give us this information in your initial post?

    In your diagram, where you show the 6" width, move down that width line a bit,
    such as to form a small triangle (all green!); this will be a right triangle with one leg = 6.

    Then, drop a perpendicular line from the right end of the 25" line to the bottom of trapezoid;
    this will leave you with a right triangle with a leg = 13 (on base line of trapezoid) and with
    hypotenuse = 18.384. Do you see/understand why the leg = 13 ?

    The 2 triangles created above are SIMILAR triangles. So you can easily calculate the remaining
    2 sides of the smaller triangle.

    Are you able to do and understand the above? If so, you probably can finish this up on your own.
    If not, ya'll come back now hear...
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