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)