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In the figure above, segment BD has length 6. What is the length

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In the figure above, segment BD has length 6. What is the length  [#permalink]

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New post 30 Mar 2017, 21:37
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A
B
C
D
E

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  95% (hard)

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30% (02:12) correct 70% (02:29) wrong based on 138 sessions

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In the figure above, segment BD has length 6. What is the length of segment AC?
A. The area of quadrilateral ABCD is 60.
B. The length of segment AD is 10.

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Re: In the figure above, segment BD has length 6. What is the length  [#permalink]

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New post 30 Mar 2017, 23:34
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Hi Godot53,

One cardinal rule that will serve you well while solving Geometry questions on the GMAT is to 'never make assumptions'. While solving Ds questions, do not go by how the diagram looks to you, but instead look for definite pieces of information provided in the questions stem and the diagram.

The definite pieces of information provided here are
1. Angle ABD and BDC are 90 degrees

If we analyze this piece of information in depth, then we can definitely say that the lines AB and DC are parallel. When a transversal (in this case BD) cuts two lines (in this case AB and DC), the two lines are said to be parallel if ONE of the three conditions are satisfied:

1. Alternate angles are equal
2. Corresponding angles are equal
3. Sum of the interior angles is 180 degrees

Attachment:
Screenshot.png
Screenshot.png [ 38.79 KiB | Viewed 1988 times ]


So here since we have angles ABD and BDC to be 90 degrees, the sum of interior angles will be 180 degrees. This makes lines AB and DC parallel.

ABCD is therefore a trapezoid whose bases are AB and CD and whose perpendicular height is BD=6.

Area of a trapezoid = (Sum of parallel sides)/2 * h

Thus, area of trapezoid ABCD = (AB+CD)/2 * 6 = 3(AB+CD)

Attachment:
Screenshot 2.PNG
Screenshot 2.PNG [ 14.34 KiB | Viewed 1988 times ]


In the figure above, since AO is perpendicular to CO, quadrilateral ABDO is a rectangle and ∆ACO is a right triangle

In rectangle ABDO, AO = BD =6 and DO = AB.

OC = OD+CD ------> OC = AB + DC .

Since ∆ACE is a right triangle, AO^2 + OC^2 = AC^2 ------> 6^2 + OC^2 = AC^2.

So here we just need the length of OC or the length of AB + DC.

Statement 1: The area of quadrilateral ABCD is 60

3(AB+CD) = 60
AB+CD = 20. SUFFICIENT.

Statement 2: AD =10


Using this information we can find out AB, but we still do not know the length of DC. INSUFFICIENT.

Answer : A

Hope this helps!

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Re: In the figure above, segment BD has length 6. What is the length  [#permalink]

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New post 25 Aug 2018, 21:43
Given: BD=6

Statement 1: The area of quadrilateral ABCD is 60.
Let the point where AC intersects BD be X. So, BD= BX + XD

The area of quadrilateral ABCD= Area of Triangle ABC + Area of Triangle ADC
Area of Triangle ABC= (1/2)*AC*BX
Area of Triangle ADC= (1/2)*AC*XD

On Adding, we get
Area of Triangle ABC + Area of Triangle ADC= (1/2)*AC*BX + (1/2)*AC*XD
Taking (1/2)*AC Common, we get
The area of quadrilateral ABCD= Area of Triangle ABC + Area of Triangle ADC= (1/2)*AC*[BX+DX]
60 = (1/2)*AC*BD
60= (1/2)*AC*6

We can solve for AC.
Hence, Sufficient.

Statement 1:The length of segment AD is 10.

Using AD, we can Find BC but nothing else.
hence Insufficient.

Therefore, our Answer is A.

godot53 wrote:
Attachment:
Capture.PNG


In the figure above, segment BD has length 6. What is the length of segment AC?
A. The area of quadrilateral ABCD is 60.
B. The length of segment AD is 10.

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Re: In the figure above, segment BD has length 6. What is the length &nbs [#permalink] 25 Aug 2018, 21:43
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In the figure above, segment BD has length 6. What is the length

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