Question

Which set of line segments can be used to construct a triangle?

A) 2 cm, 6 cm, and 1 cm
B) 3 cm, 3 cm, and 2 cm
C) 4 cm, 2 cm, and 8 cm
D) 4 cm, 3 cm, and 9 cm

Answer 1

Option B

Explanation:

Option A

In order to make a triangle: a + b > c and b + c > a and c + a > b

2 is a, 6 is b, and 1 is c

a + b > c

2 + 6 > 1

8 > 1 -> TRUE

b + c > a

6 + 1 > 2

7 > 2 -> TRUE

c + a > b

1 + 2 > 6

3 > 6 -> FALSE

Option B

In order to make a triangle: a + b > c and b + c > a and c + a > b

3 is a, 3 is b, 2 is c

a + b > c

3 + 3 > 2

6 > 2 -> TRUE

b + c > a

3 + 2 > 3

5 > 3 -> TRUE

c + a > b

2 + 3 > 3

5 > 3 -> TRUE

OPTION B IS A TRIANGLE

Option C and D are automatically incorrect because Option B is incorrect. But, the same process would go to the end.

Answer: Option B