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

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.

IIM CAT Preparation Tips: CAT Geometry

Jun 13, 2013

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

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.