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)

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