Which set of line segments can be used to construct a triangle? A) 2 cm, 8 cm, and 9 cm B) 3 cm, 6 cm, and 2 cm C) 5 cm, 9 cm, and 3 cm D) 6 cm, 3 cm, and 10 cm

Answer:It's not A, I got it wrong it's B 3cm, 3cm, and 2cm.

Answer: option A is the correct answer

Step-by-step explanation:

The set of line segments that can be used is the one such that, its longest side is lesser than the semi perimeter, s[s = (a+b+c) / 2] of the triangle.

If we apply this condition on the given line segments,

A) 2 cm, 8 cm, and 9 cm

s = (2+8+9) / 2 = 9.5

9.5 is greater than 9cm

B) 3 cm, 6 cm, and 2 cm

s = (3+6+2) / 2 = 5.5

5.5 is lesser than 6. If we go on to look for the area using

Area = √s (s-a) (s-b) (s-c), it would be impossible because we would end up having square root of a negative number.

C) 5 cm, 9 cm, and 3 cm

s = (5+9+3) / 2 = 8.5

8.5 is lesser than 9cm

If we go on to look for the area using

Area = √s (s-a) (s-b) (s-c), it would be impossible because we would end up having square root of a negative number.

D) 6 cm, 3 cm, and 10 cm

s = (6+3+10) / 2 = 9.5

9.5 is lesser than 10

If we go on to look for the area using

Area = √s (s-a) (s-b) (s-c), it would be impossible because we would end up having square root of a negative number.

So option A is the correct answer