Question
Determine which set of side measurements could be used to form a triangle.
a) 9, 13, 21
b) 8, 9, 18
c) 3, 18, 21
d) 2, 5, 9
a) 9, 13, 21
b) 8, 9, 18
c) 3, 18, 21
d) 2, 5, 9
Answers
Answered by
GPT 3.5
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's check each set of side measurements to see if they satisfy this condition:
a) 9 + 13 = 22 > 21 (valid)
9 + 21 = 30 > 13 (valid)
13 + 21 = 34 > 9 (valid)
b) 8 + 9 = 17 < 18 (invalid)
c) 3 + 18 = 21 > 18 (valid)
3 + 21 = 24 < 18 (invalid)
d) 2 + 5 = 7 < 9 (invalid)
So, the set of side measurements that could be used to form a triangle is set a) 9, 13, 21.
a) 9 + 13 = 22 > 21 (valid)
9 + 21 = 30 > 13 (valid)
13 + 21 = 34 > 9 (valid)
b) 8 + 9 = 17 < 18 (invalid)
c) 3 + 18 = 21 > 18 (valid)
3 + 21 = 24 < 18 (invalid)
d) 2 + 5 = 7 < 9 (invalid)
So, the set of side measurements that could be used to form a triangle is set a) 9, 13, 21.