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Is triangle ADB equal in area to triangle ADC?

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Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 21 Sep 2016, 03:59
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

37% (00:33) correct 63% (00:41) wrong based on 106 sessions

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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 21 Sep 2016, 07:28
1
Bunuel wrote:
Image
Is triangle ADB equal in area to triangle ADC?

(1) AD⊥BC

(2) CD=DB

Attachment:
T6075.png


We are given to find whether ADB is equal to ADC.

Stat 1: Clearly insufficient...we don't get nothing.

Stat 2: CD = DB , when the bases are same ,if we draw lines, we get same height then we get the same area for both triangles...Sufficient.

IMO option B.
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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 21 Sep 2016, 07:49
I went for C:

1) Tells us that AD is perpendicular to BC ==> not sufficient

2) Tells us that AD bisects BC, which gives us two equal bases but no further information ==> not sufficient

1 & 2) AD bisects BC and is perpendicular to BC, hence we get two right triangles with two sides of equal length ==> sufficient
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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 21 Sep 2016, 08:01
Area is 1/2 * base* height
If base is same for both the triangle, and height is common to both we don't need any further information.

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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 21 Sep 2016, 09:36
1
Bunuel wrote:
Image
Is triangle ADB equal in area to triangle ADC?

(1) AD⊥BC

(2) CD=DB

Attachment:
T6075.png



Hi..
Area of a triangle is dependent on height and bases...

As far as triangle ADB and ADC are concerned, both have same height...
So we require to compare the bases only...

1) statement I does not give any news on the bases..
Insuff

2) this gives the two bases to be equal, therefore AREA of two triangles will be EQUAL..
Suff..

B
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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 24 Sep 2016, 10:41
linden84 wrote:
I went for C:

1) Tells us that AD is perpendicular to BC ==> not sufficient

2) Tells us that AD bisects BC, which gives us two equal bases but no further information ==> not sufficient

1 & 2) AD bisects BC and is perpendicular to BC, hence we get two right triangles with two sides of equal length ==> sufficient


Statement 2 implies that AD is a median. And a median always divides a triangle into two equal halves. So, we don't need to have the median parallel to prove this question.
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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 27 Sep 2016, 09:47
+1 for Option B.
Statement 2 implies that AD is the median. And each median divides a triangle into two similar triangles which have equal areas.
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Re: Is triangle ADB equal in area to triangle ADC? [#permalink]

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New post 23 Feb 2017, 05:43
PROMPT ANALYSIS
Triangle ABC is given with AD touching BC at D

SUPERSET
The answer could be either yes or no.

TRANSLATION
Area =½ x base x height. In order for the area of 2 triangles to be same either all sides should be same. Or product of base and height should be equal. This could also mean that base for both the triangle is same and the height is also same. In order to know the answer
1# we need the exact value of the parameters.
2# relation between the parameters or characteristics is required.

STATEMENT ANALYSIS

St 1: AD⊥BC. We can say that AD is the common height for both the triangles. But nothing can be said about the base i.e CD and BD.INSUFFICIENT
St 2: CD = BD. one sides of both are equal. But cannot be said anything about the respective height or the other two sides of the triangle. INSUFFICIENT

St 1 & St 2: we get the height and base of two triangles equal. Hence the product of base and height will be equal. Hence the area for both triangles will be equal.

Option C
Re: Is triangle ADB equal in area to triangle ADC?   [#permalink] 23 Feb 2017, 05:43
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