Question

a, b, c are integers that are the side of an obtuse-angled triangle. If ab = 8, find c.

1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 3 : 3

Calculation:

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 third side has to be a 3.