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24 Feb 2023, 02:30
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
41% (01:03) correct
59%
(01:02)
wrong
based on 37
sessions
History
Date
Time
Result
Not Attempted Yet
Is triangle ADB equal in area to triangle ADC?
(1) AD⊥BC
(2) CD=DB
700-Level Question!!!
Attachment:
1 (7).png [ 3.17 KiB | Viewed 1954 times ]
24 Feb 2023, 03:37
Kudos
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Is triangle ADB equal in area to triangle ADC?
(1) AD⊥BC => AD is height of both the triangles
area of triangle ADB = (1/2)*BD*AD
are of triangle ADC = (1/2)*CD*AD
Since we don't know whether BD = CD, so we can't say if the area of the triangles are equal.
Not sufficient.
(2) CD=DB
area of triangle ADB = (1/2)*BD*ht
are of triangle ADC = (1/2)*CD*ht
Since the triangles base are equal (CD=DB) and they share common third point, the height of these triangles are common/equal.
Therefore, we know that the two triangles have equal area.
Statement 2 alone is Sufficient.
See the attached diagram.
Answer B
(1) AD⊥BC => AD is height of both the triangles
area of triangle ADB = (1/2)*BD*AD
are of triangle ADC = (1/2)*CD*AD
Since we don't know whether BD = CD, so we can't say if the area of the triangles are equal.
Not sufficient.
(2) CD=DB
area of triangle ADB = (1/2)*BD*ht
are of triangle ADC = (1/2)*CD*ht
Since the triangles base are equal (CD=DB) and they share common third point, the height of these triangles are common/equal.
Therefore, we know that the two triangles have equal area.
Statement 2 alone is Sufficient.
See the attached diagram.
Answer B
Attachments
Picture1.jpg [ 172.3 KiB | Viewed 1459 times ]
25 Feb 2023, 07:38
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Bunuel
Solution:
Pre Analysis:
- We are asked if area of triangle ADB is equal to area of triangle ADC or not
Statement 1: \(AD⊥BC\)
- If \(AD⊥BC\), then
- Area of triangle ADB \(=\frac{1}{2}\times DB\times AD\)
- Area of triangle ACD \(=\frac{1}{2}\times CD\times AD\)
- For both the areas to be same, sides DB and CD have to be equal which we don't know of
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(CD=DB\)
- According to this statement, the bases of both the triangles are equal
- We can infer that the height of both the triangles will also be equal because it is falling on the respective bases from same point A
- This means we can say that both the areas will also be same
Hence the right answer is Option B
