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In the figure shown, ABCD is a trapezium. What is the value of x?

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In the figure shown, ABCD is a trapezium. What is the value of x?  [#permalink]

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23 Dec 2018, 03:07
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In the figure shown, ABCD is a trapezium. What is the value of x?

A. $$\frac{-11}{3}$$
B. $$-2$$
C. $$2$$
D. $$3$$
E. $$11$$

Source: Experts Global

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Re: In the figure shown, ABCD is a trapezium. What is the value of x?  [#permalink]

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23 Dec 2018, 05:23
1
Triangle OAB is similar to triangle OCD ( As AB is parallel to CD)
hence, OA/OC = OB/OD
2/2 =3/ (5-X)
Hence, x = 2

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Re: In the figure shown, ABCD is a trapezium. What is the value of x?  [#permalink]

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24 Dec 2018, 22:06
1
OAB ~ OCD using ASA similarity (Angle-Side-Angle), because
angle AOB = angle COD (vertically opposite)
side AO = side CO
angle OAB = angle OCD (interior alternate angles as AB II DC )

So ratio of sides of both triangles is equal
AO:CO = BO: DO
2:2 = 3:5-x

==> 1= 5-x/3
x=2

Re: In the figure shown, ABCD is a trapezium. What is the value of x?   [#permalink] 24 Dec 2018, 22:06
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In the figure shown, ABCD is a trapezium. What is the value of x?

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