# CAT Practice : Coordinate Geometry

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If a triangle has sides a, b, and c one should be able to say whether the triangle is right, obtuse-angled or acute-angled. If we are told a given triangle is obtuse-angled what might we infer from that?

## Triangles - Integer values

Q.1: x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z.
1. 2
2. 3
3. 1
4. More than one possible value of z exists

Choice (B). 3

## Detailed Solution

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.

1. 221 is acute. 12 + 22 > 22
2. 222 is equilateral. So acute.
3. 223 is obtuse. 22 + 22 < 32
4. 144 is acute. 12 + 42 > 42
Only triangle 223 is obtuse. Hence, the third side has to be 3.

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.