Anonymous

# can anyone solve this geometry??

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

AB = BD

CD = 21 cm

B = 120 degrees

BD = ?

Relevance

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.

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

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

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!