Which of the following measures can form a triangle?
3, 4, 6
Concept:
The sum of two sides of a triangle must be greater than the length of the third side.
Calculation:
Option 1:
2 + 3 < 6
5 < 6
⇒ The sum of the two sides of the triangle is less than the length of the third side.
This option is incorrect.
Option 2:
3 + 4 > 6
7 > 6
4 + 6 > 3
10 > 3
3 + 6 > 4
9 > 4
The sum of the two sides of the triangle must be greater than the length of the third side.
This option is correct.
3 + 4 = 7
The sum of the two sides of the triangle is equal to the length of the third side.
This option is incorrect.
4 + 6 < 12
10 < 12
⇒ The sum of the two sides of the triangle is less than the length of the third side.
This option is incorrect.
Option: 2 is correct.
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