CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions

The question is from CAT Geometry - Triangles. CAT exam is known to test on multiple ideas in the same question, so you should be ready to face them. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. 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?

Question 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

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Explanatory Answer

Method of solving this CAT Question from Geometry - Triangles: Checking out the possibilities of the third side will give the answer.

xy = 4
xy could be 2 *2 or 4 * 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

The question is " x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z."
And so, the third side has to be 3

Hence, the answer is 3.

Choice B is the correct answer.