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08 Apr 2021, 11:00
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A
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Difficulty:
65%
(hard)
Question Stats:
20% (00:46) correct
80%
(01:46)
wrong
based on 50
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of triangle EBC?
(1) The area of ΔAED is 16.
(2) The area of ΔDEC is 12.
Attachment:
1.png [ 3.78 KiB | Viewed 2746 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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08 Apr 2021, 11:20
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Asked: What is the area of triangle EBC?
The area of ΔADC = The area of ΔBDC
since they have same base and height
The area of ΔADC = The area of ΔAED + The area of ΔEDC
The area of ΔBDC = The area of ΔEBC + The area of ΔEDC
The area of ΔAED + The area of ΔEDC = The area of ΔEBC + The area of ΔEDC
The area of ΔAED = The area of ΔEBC
(1) The area of ΔAED is 16.
The area of ΔAED = 16 = The area of ΔEBC
SUFFICIENT
(2) The area of ΔDEC is 12.
The area of ΔEBC can not be derived from the information.
NOT SUFFICIENT
IMO A
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24 Mar 2022, 00:25
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Official Explanation:
The issue is finding the area of triangle EBC.
The area of a triangle is ½×BASE×HEIGHT. Therefore, two triangles with the same base and an equal height will have equal areas. ΔACD and ΔBCD share the same base CD. As to the height:
The height of triangle ADC is AD, while the height of triangle DBC is a line drawn from the vertex B and perpendicular to the extension of side DC: In an obtuse triangle the height may be found outside the triangle, so that it is perpendicular to the extension of the side. However, since angles A and D are right angles, lines AB and CD are parallel, and any height drawn between them will be equal for both ΔACD and ΔBCD. Hence the height of ΔACD is equal to the height of ΔBCD.
Since The two triangles share the same base and have equal heights, the area of ΔACD=The area of ΔBCD.
The issue is finding the area of triangle EBC.
The area of a triangle is ½×BASE×HEIGHT. Therefore, two triangles with the same base and an equal height will have equal areas. ΔACD and ΔBCD share the same base CD. As to the height:
The height of triangle ADC is AD, while the height of triangle DBC is a line drawn from the vertex B and perpendicular to the extension of side DC: In an obtuse triangle the height may be found outside the triangle, so that it is perpendicular to the extension of the side. However, since angles A and D are right angles, lines AB and CD are parallel, and any height drawn between them will be equal for both ΔACD and ΔBCD. Hence the height of ΔACD is equal to the height of ΔBCD.
Since The two triangles share the same base and have equal heights, the area of ΔACD=The area of ΔBCD.
