Bunuel wrote:
Which of the following can be the ratio of sides of a triangle?
I. \(3:\sqrt{4}:5\)
II. \(\sqrt{3}:4:5\)
III. \(3:4:\sqrt{5}\)
A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
The sum of any two sides of a triangle must be greater than the third side.
I. \(3:\sqrt{4}:5\)
The ratio of sides are 3, 2 and 5
But 3 + 2 = 5 which is not acceptable. The sum of any two sides must be greater than the third side.
Hence these cannot be the ratio of the sides of the triangle.
II. \(\sqrt{3}:4:5\)
The ratio of sides are 1.7, 4 and 5.
The sum of any two is greater than the third.
So these can be the ratio of the sides of the triangle.
III. \(3:4:\sqrt{5}\)
The ratio of sides are 3, 4 and 2.2
The sum of any two is greater than the third.
So these can be the ratio of the sides of the triangle.
Answer (D)
Is it sufficient to just check for condition - The sum of any two is greater than the third.
or do we also have to check that the difference of any two sides should be less than the third side