Final answer:
According to the Triangle Inequality Theorem, option B) 6 yds., 8 yds., 13 yds. can be the lengths of the sides of a triangle.
Step-by-step explanation:
In order for a set of numbers to be the lengths of the sides of a triangle, they must satisfy the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's examine each option:
A) 5 m, 9 m, 18 m: The sum of the lengths of the smaller sides (5 m and 9 m) is 14 m, which is less than the length of the longest side (18 m). Therefore, this set of numbers cannot be the lengths of the sides of a triangle.
B) 6 yds., 8 yds., 13 yds.: The sum of the lengths of the smaller sides (6 yds. and 8 yds.) is 14 yds., which is greater than the length of the longest side (13 yds.). Therefore, this set of numbers can be the lengths of the sides of a triangle.
C) 7 ft., 8 ft., 16 ft.: The sum of the lengths of the smaller sides (7 ft. and 8 ft.) is 15 ft., which is less than the length of the longest side (16 ft.). Therefore, this set of numbers cannot be the lengths of the sides of a triangle.
Based on the Triangle Inequality Theorem, option B) 6 yds., 8 yds., 13 yds., can be the lengths of the sides of a triangle.