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10 May 2018, 01:39
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D
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Difficulty:
55%
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Question Stats:
59% (01:56) correct
41%
(02:34)
wrong
based on 211
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In the figure, what is the area of triangle BCD given that the area of triangle ADE is 16 and the area of triangle CDE is 12?
A) 12
B) 16
C) 20
D) 28
E) Cannot be determined
Attachment:
FIGURE.jpg [ 24.33 KiB | Viewed 13429 times ]
10 May 2018, 05:42
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Solution
Given:
• Area of triangle ADE = 16
• Area of triangle CDE = 12
To find:
• What is the area of triangle BCD
Approach and Working:
• As the triangles ACD and BCD share the same base DC, and their height is also same, they have equal area
• Therefore, the area of triangle BCD = area of triangle ACD = area of triangle ADE + area of triangle CDE = 16 + 12 = 28
Hence, the correct answer is option D.
Answer: D
Updated on: 28 Apr 2021, 06:41
Originally posted by BrentGMATPrepNow on 19 Oct 2018, 14:01.
Last edited by BrentGMATPrepNow on 28 Apr 2021, 06:41, edited 1 time in total.
Last edited by BrentGMATPrepNow on 28 Apr 2021, 06:41, edited 1 time in total.
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Bunuel
In the figure, what is the area of triangle BCD given that the area of triangle ADE is 16 and the area of triangle CDE is 12?
A) 12
B) 16
C) 20
D) 28
E) Cannot be determined
Attachment:
FIGURE.jpg
∆ADC is comprised of 2 regions: ∆ADE and ∆CDE
We're told that ∆ADE and ∆CDE have areas 16 ans 12 respectively.
So, the area of ∆ADC = 16 + 12 = 28
First recognize that ∆ADC and ∆BCD both have the same base.
Also, if we let h = the height of ∆ADC, then ∆BCD also has height h
area of triangle = (base)(height)/2
So, if ∆ADC and ∆BCD have the same base and the same height, then they must have the same area.
So, if the area of ∆ADC is 28, then the area of ∆BCD must also be 28
Answer: D
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