Which of the following sets of side lengths can be used to draw a triangle? Remember the triangle inequality theorm.
2 cm, 3 cm, 6 cm
6 cm, 5 cm, 10 cm
7 cm, 9 cm, 16 cm
10 cm, 10 cm, 20 cm
The triangle inequality theorem states that for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Looking at the sets of side lengths given:
1) 2 cm, 3 cm, 6 cm
2 + 3 = 5, which is less than 6.
This set of side lengths cannot be used to draw a triangle.
2) 6 cm, 5 cm, 10 cm
6 + 5 = 11, which is greater than 10.
5 + 10 = 15, which is greater than 6.
10 + 6 = 16, which is greater than 5.
This set of side lengths can be used to draw a triangle.
3) 7 cm, 9 cm, 16 cm
7 + 9 = 16, which is equal to 16.
This set of side lengths cannot be used to draw a triangle.
4) 10 cm, 10 cm, 20 cm
10 + 10 = 20, which is equal to 20.
This set of side lengths cannot be used to draw a triangle.
Based on the triangle inequality theorem, the only set of side lengths that can be used to draw a triangle is: 6 cm, 5 cm, 10 cm.