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)