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13 May 2019, 02:45
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E
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Difficulty:
85%
(hard)
Question Stats:
50% (03:22) correct
50%
(02:54)
wrong
based on 54
sessions
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All of the triangles in the diagram below are similar to isosceles triangle ABC, in which AB = AC. Each of the 7 smallest triangles has area 1, and triangle ABC has area 40. What is the area of trapezoid DBCE?
A. 16
B. 18
C. 20
D. 22
E. 24
Attachment:
d13adfd6d388ea5d30660f97f3b425db198e8093.png [ 11.75 KiB | Viewed 12359 times ]
13 May 2019, 04:04
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triangle AFG is similar to triangle ADE
Area AFG/ Area ADE = FG^2/DE^2= (3x^2)/4x^2) =9/16
If, Area of AFG= 9k Then Area of ADE = 16k
Area of ADE - Area of AFG = 7k which is equal to 7 small isosceles triangles
Hence 7k= 7*1 or k=1
Area of ADE=16k=16
Trapezium DEBC = Area of ABC - Area of ADE= 40-16=24
Area AFG/ Area ADE = FG^2/DE^2= (3x^2)/4x^2) =9/16
If, Area of AFG= 9k Then Area of ADE = 16k
Area of ADE - Area of AFG = 7k which is equal to 7 small isosceles triangles
Hence 7k= 7*1 or k=1
Area of ADE=16k=16
Trapezium DEBC = Area of ABC - Area of ADE= 40-16=24
Bunuel
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d13adfd6d388ea5d30660f97f3b425db198e8093.png [ 13.32 KiB | Viewed 11006 times ]
02 Aug 2019, 01:43
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The biggest clue which is given in this question is about the similarity of the triangles in the figure.
If two triangles are similar, the ratio of their areas will be equal to the square of the ratio of their corresponding sides.
This is the concept that will help us solve this question. Take a look at this diagram which details the solution for this question:
2nd Aug 2019 - Reply 2.JPG [ 77.59 KiB | Viewed 10597 times ]
When the question mentions similar triangles and their areas in the same breath, always remember to use the concept mentioned above. And for you to be able to do that, you will have to be able to identify the corresponding sides in the similar triangles, for which you need to identify the equal angles in turn.
In this case, since it is mentioned that all the smaller triangles are equal, we could conclude that DE = 4 * DX. Had this information not been given, this question could have been a lot more difficult to handle.
The correct answer option is E.
Hope this helps!
If two triangles are similar, the ratio of their areas will be equal to the square of the ratio of their corresponding sides.
This is the concept that will help us solve this question. Take a look at this diagram which details the solution for this question:
Attachment:
2nd Aug 2019 - Reply 2.JPG [ 77.59 KiB | Viewed 10597 times ]
When the question mentions similar triangles and their areas in the same breath, always remember to use the concept mentioned above. And for you to be able to do that, you will have to be able to identify the corresponding sides in the similar triangles, for which you need to identify the equal angles in turn.
In this case, since it is mentioned that all the smaller triangles are equal, we could conclude that DE = 4 * DX. Had this information not been given, this question could have been a lot more difficult to handle.
The correct answer option is E.
Hope this helps!
