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![Is triangle ABC an acute angled triangle? 1) [m]c^2 < a^2 + b^2[/m] w](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Is triangle ABC an acute angled triangle? 1) [m]c^2 < a^2 + b^2[/m] w"){kind=icon}
31 Oct 2018, 07:40
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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:
75%
(hard)
Question Stats:
32% (01:21) correct
68%
(01:13)
wrong
based on 65
sessions
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Is triangle ABC an acute angled triangle?
1) \(c^2 < a^2 + b^2\) where a, b and c are sides of triangle ABC
2) Sides of the triangle ABC have lengths 5, 6 and 7
Source: www.GMATinsight.com
1) \(c^2 < a^2 + b^2\) where a, b and c are sides of triangle ABC
2) Sides of the triangle ABC have lengths 5, 6 and 7
Source: www.GMATinsight.com
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:
Data Sufficiency Forum
Data Sufficiency Forum
31 Oct 2018, 08:19
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CONCEPT:
If \(a^2+b^2 < c^2\), it means the angle between side a & b is obtuse, the triangle is obtuse.
If \(a^2+b^2 > c^2\), it means the angle between a & b is acute, but since other angle can be obtuse, the triangle cant be taken as acute.
If \(a^2+b^2 =c^2\), it means the angle between a & b is 90 deg, hence the triangle is right.
St1)
\(a^2+b^2 > c^2\), it means the angle between a & b is acute, but since other angle can be acute/obtuse, the triangle cant be taken as acute.
NOT SUFFICIENT.
St2) Sides of the triangle ABC have lengths 5, 6 and 7
As all the sides are known, a unique triangle can be made and hence angle can be found.
So, we can say whether the triangle is acute or not.
SUFFICIENT.
Answer = B
To understand better, please see sketch
Attachment:
gmatbusters.jpg [ 120.19 KiB | Viewed 3015 times ]
GMATinsight
31 Oct 2018, 14:06
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GMATinsight
All angles are measured in degrees.
\({\rm{all}}\,\,\Delta ABC\,\,{\rm{internal}}\,\,{\rm{angles}}\,\,\mathop < \limits^? \,\,\,{90}\)
We assume c is the length of the side that is opposite to the internal angle ACB, etc.
\(\left( 1 \right)\,\,\,\,{c^2} < {a^2} + {b^2}\,\,\,\, \Rightarrow \,\,\,\,\,\angle ACB < 90\,\,\,\, \Rightarrow \,\,\,\,{\rm{INSUFF}}.\)
\(\left( 2 \right)\,\,\,5,6,7\,\,\,\,\, \Rightarrow \,\,\,\,\,\Delta ABC\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta ABC\,\,{\rm{internal}}\,\,{\rm{angles}}\,\,{\rm{are}}\,\,{\rm{uniquely}}\,\,{\rm{known}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\,\,\,\)
POST-MORTEM:
\({7^2} < {5^2} + {6^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\max \,\,\,\Delta ABC\,\,{\rm{internal}}\,\,{\rm{angle}}\,\,\,\, < \,\,90\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
01 Nov 2018, 04:18
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GMATinsight
A question on similar property can be seen here
https://gmatclub.com/forum/in-the-diagr ... l#p2158190
The concept of the acute angled, Right angles and Obtuse angled triangle is as shown in the file attached.
Please pay attention to the fact that here c is representing the longest side of the triangle
Attachments
File comment: www.GMATinsight.com
Geometry 3 Right Acute and Obtuse angle triangle.jpg [ 96.22 KiB | Viewed 2791 times ]
