If a triangle has sides a, b, and c one should be able to say whether the triangle is right, obtuse-angled or acute-angled. If we are told a given triangle is obtuse-angled what might we infer from that?
Triangles - Integer values
Q.1: x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z.
2
3
1
More than one possible value of z exists
Correct Answer
Choice (B). 3
Detailed Solution
xy = 4
xy could be 2 x 2 or 4 x 1
221
222 These are the possible triangles.
223
441
22x will be a triangle if x is 1, 2 or 3 (trial and error).
44x is a triangle only if x is 1.
221 is acute. 1^{2} + 2^{2} > 2^{2}
222 is equilateral. So acute.
223 is obtuse. 2^{2} + 2^{2} < 3^{2}
144 is acute. 1^{2} + 4^{2} > 4^{2}
Only triangle 223 is obtuse. Hence, the third side has to be 3.
Correct Answer: 3
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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.