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In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals

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In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

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New post 31 Jul 2016, 02:08
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In a trapezium ABCD, AB is parallel to DC, AB = 3*DC, and the diagonals of the trapezium intersect at O. The ratio of the area of ∆OCD to the area of ∆OAB is:

(A) 1:9
(B) 1:3
(C) 3:1
(D) 1:10
(E) Cannot be determined

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Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

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New post 31 Jul 2016, 02:56
triangles are similar , so ratio will be 1:9

A
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Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

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New post 31 Jul 2016, 22:58
Can someone please explain how the diagonal properties of trapezoid. I am not sure how the two triangles would be similar in this case
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Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

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New post 03 Aug 2016, 09:24
hsbinfy wrote:
triangles are similar , so ratio will be 1:9

A



AB||DC
A=(base1+base2/2)*h
ratio will change as height changes, no?
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Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

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New post 14 Apr 2017, 01:13
1
3
inshor

In Triangle AOB and Triangle COD
Angle AOB = Angle COD (Vertical Angles)
Other two angles are formed between a pair of parallel line AB || DC
Angle BAO = Angle DCO (Alternate interior angle)
Angle ABO = Angle CDO (Alternate interior angle)

Therefore, by AAA Property the two triangle are similar

The ratio of a side is already given, i.e. 1:3

The ratio of their areas will be square of the ratio of their sides (Property of similar triangles)
Ans - 1^2 : 3^2 = 1:9
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Re: in a trapezium ABCD , AB is parallel to DC , AB = 3DC , and  [#permalink]

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New post 29 Jan 2019, 04:31
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Re: in a trapezium ABCD , AB is parallel to DC , AB = 3DC , and   [#permalink] 29 Jan 2019, 04:31
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In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals

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