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Finding the sides of a trapedzoid using only Angles and perimeter

  1. Sep 12, 2012 #1
    1. The problem statement, all variables and given/known data
    My knowns are: the trapezoid has a perimeter equal to 180 inches
    and it's base angles are ∏/3

    The unknowns are: the lengths of the base (x) and the length of one of the slanted sides (y)
    as well as the relationship between x and y

    2. Relevant equations
    Trig equations


    3. The attempt at a solution
    I pretty much split up the trapezoid into 2 right triangles and a rectangle. The triangle creates a 30-60-90 right triangle giving me the length ratios of the sides. This is where I hit my dead end because I have no idea how to find the lengths of the triangles without a single length of any of the triangle's sides. My friend was able to guess and check the correct lengths of x=75 inches and y=30 inches.

    I want to know if it's possible to find any of the unknown sides without having to resort to a guess and check method. Also I'm not sure, when it says to deduce a relationship between x and y if it means to create some sort of formula that relates them or something.

    Any insight on this is appreciated and thanks in advance.
     
  2. jcsd
  3. Sep 12, 2012 #2

    LCKurtz

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    If you call the base of each of your triangles ##b## don't you see that ##b=y/2##? So you can get the top side in terms of ##x## and ##y##. So with all sides in terms of ##x## and ##y##, write the equation of the perimeter. I think you will find your friends answer is not the only one.
     
  4. Sep 13, 2012 #3
    I don't completely get your answer, but then it maybe because I'm at fault for poor wording and that my x-value was off. My x=70 had a lapse in thinking for a bit and I may need to clarify what's x and y. The x unknown is the longer base of the trapezoid and the y unknown is the side of the trapezoid.

    I broke down the trapezoid into 2 triangles and a single rectangle so that now my y is equal to the triangle's hypotenuse and the x is equal to y + the base of the rectangle on its (rectangle) longer side. The reason x=y + rectangle base is because the short-side of the triangle is equal to the hypotenuse/2 and that 2 would end up being canceled out because there are 2 equal triangles.

    I'm sorry if I did not seem as clear, when I first posted my query.
     
  5. Sep 13, 2012 #4
    Okay getting some time to look at it now I see your point and was able to simplify the expression down to [itex] x = 90 - y/2[/itex]
     
  6. Sep 13, 2012 #5

    LCKurtz

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    Correct.
     
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