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Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

can anyone solve this geometry??

imagine there's a trapezium ABDC......

AB = BD

CD = 21 cm

B = 120 degrees

BD = ?

4 Answers

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  • 1 decade ago
    Favorite Answer

    first, i want to ask you, where do you live?

    Are you in US or in England?

    Why?

    Coz these two countries have different definition of trapezoid and trapezium.

    According to US

    trapezoid is a quadrilateral with one pair of parallel sides.

    trapezium is a quadrilateral with no pair of parallel sides.

    While in England

    trapezoid is a quadrilateral with no pair of parallel sides.

    trapezium is a quadrilateral with one pair of parallel sides.

    which one is your question.

    If your thinking of a quadrilateral with no pair of parallel sides,

    there is no asnwer to your question.

    actually, there is, but the solutions is actually a family of curves.

    If your thinking of a quadrilateral with one pair of parallel sides,

    here's the solution:

    i assume that sides AB and CD are parallel sides since you did not specify which one is the paralle sides.

    By inspection, the trapezoid is actually an equilateral trapezoid.

    if this is the case, we can conclude that

    AB = BC = AD

    Now taking the right triangle on its side, we get

    hypotenuse = x

    base = (21-x)/2

    actually, the triangle is a 30-60-90 triangle.

    according to this, the base is half of the hypotenuse.

    thus,

    [(21-x)/2]/2 = x

    21-x=4x

    solving for x, we get

    x = 21/5

    AC = BD

    by using cosine law

    AC^2 = x^2 + x^2 - 2x^2 cos 120

    AC^2 = x^2 + x^2 + x^2

    AC^2 = 3x^2

    AC = x sqrt(3)

    since x = 21/5

    AC = (21/5) * sqrt(3)

    therefore

    BD = (21/5) * sqrt(3)

    BD = 7.274613392

    sorry, it took time to finish my novel.

    hehehehe

  • 1 decade ago

    Imagine the trapezioid ABCD.

    By geometric inspection, similar angles, and sine rule(see below)

    sin60/DB = sin45/21 >>>hence DB=18.82

    If I drew it as in your book, it should be right.

    Source(s): my brain!
  • 1 decade ago

    Here is a math related site for you to figure out.

    http://mathworld.wolfram.com/Trapezium.html

    Source(s): internet
  • 1 decade ago

    i know! i know! YOU CAN!! good luck! :D

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