CAT Geometry

 
Question
 x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z.
 
A.    2
B.    3
C.    1
D.    More than one possible value of z exists
Answer:  Choice B
Explanatory Answer:
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.
Ø  221 is acute.  12 + 22> 22
Ø  222 is equilateral. So acute.
Ø  223 is obtuse.  22 + 22< 32
Ø  144 is acute.  12 + 42> 42 
Only triangle 223 is obtuse.  Hence, the third side has to be 3.
Answer Choice (B)

Related posts

  • CAT GeometryJune 12, 2013 CAT Geometry Question Sides of a triangle are 6, 10 and x for what value of x is the area of the D the maximum? A.    8 cms B.    9 cms C.    12 cms D.    None of these Correct Answer: […] Posted in Geometry
  • Online CAT Coaching: A few interesting True/False questions from GeometryJune 2, 2015 Online CAT Coaching: A few interesting True/False questions from Geometry State whether the following statements are true or false 1. A parallelogram that circumscribes a circle has to be a square 2. A trapezium inscribed in a circle has to be an […] Posted in Geometry
  • CAT Geometry SolutionsAugust 27, 2011 CAT Geometry Solutions Have given below the solutions to the questions on basic geometry 1. Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible? This is just a […] Posted in Geometry
  • CAT Geometry QuestionOctober 9, 2010 CAT Geometry Question Here is a good geometry question The unequal side of an isosceles triangle is thrice the inradius of the triangle. What is the ratio of the longest side to the shortest side of this […] Posted in Geometry

Leave a Reply

Your email address will not be published. Required fields are marked *