Which of the following sets of side lengths can be used to draw a triangle? Remember the Triangle Inequality Theorem.
A. 2 cm, 3 cm, 6 cm
B. 6 cm, 5 cm, 10 cm
C. 7 cm, 9 cm, 16 cm
D. 10 cm, 10 cm, 20 cm
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each set of side lengths:
A. 2 cm, 3 cm, 6 cm
The sum of the lengths of the two shorter sides is 2 + 3 = 5 cm, which is less than the length of the longest side (6 cm). Therefore, this set of side lengths cannot be used to draw a triangle.
B. 6 cm, 5 cm, 10 cm
The sum of the lengths of the two shorter sides is 6 + 5 = 11 cm, which is greater than the length of the longest side (10 cm). This set of side lengths can be used to draw a triangle.
C. 7 cm, 9 cm, 16 cm
The sum of the lengths of the two shorter sides is 7 + 9 = 16 cm, which is equal to the length of the longest side (16 cm). According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Since the sum is equal to the longest side, this set of side lengths cannot be used to draw a triangle.
D. 10 cm, 10 cm, 20 cm
The sum of the lengths of the two shorter sides is 10 + 10 = 20 cm, which is equal to the length of the longest side (20 cm). Similarly to option C, the sum being equal to the longest side means that this set of side lengths cannot be used to draw a triangle.
Therefore, the only set of side lengths that can be used to draw a triangle is B. 6 cm, 5 cm, 10 cm.