Question
Determine which set of side measurements could be used to form a triangle.
a 2, 6, 10
b 3, 18, 22
c 7, 13, 16
d 8, 7, 19
a 2, 6, 10
b 3, 18, 22
c 7, 13, 16
d 8, 7, 19
Answers
Answered by
GPT 3.5
In order for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's test each set of side measurements using this rule:
a) The sum of 2 and 6 is 8, which is less than 10. Therefore, triangle ABC cannot be formed.
b) The sum of 3 and 18 is 21, which is greater than 22. The sum of 3 and 22 is 25, which is also greater than 18. The sum of 18 and 22 is 40, which is greater than 3. Therefore, triangle ABC can be formed.
c) The sum of 7 and 13 is 20, which is greater than 16. The sum of 7 and 16 is 23, which is greater than 13. The sum of 13 and 16 is 29, which is greater than 7. Therefore, triangle ABC can be formed.
d) The sum of 8 and 7 is 15, which is less than 19. Therefore, triangle ABC cannot be formed.
From the given options, the sets of side measurements that could be used to form a triangle are b) 3, 18, 22 and c) 7, 13, 16.
Let's test each set of side measurements using this rule:
a) The sum of 2 and 6 is 8, which is less than 10. Therefore, triangle ABC cannot be formed.
b) The sum of 3 and 18 is 21, which is greater than 22. The sum of 3 and 22 is 25, which is also greater than 18. The sum of 18 and 22 is 40, which is greater than 3. Therefore, triangle ABC can be formed.
c) The sum of 7 and 13 is 20, which is greater than 16. The sum of 7 and 16 is 23, which is greater than 13. The sum of 13 and 16 is 29, which is greater than 7. Therefore, triangle ABC can be formed.
d) The sum of 8 and 7 is 15, which is less than 19. Therefore, triangle ABC cannot be formed.
From the given options, the sets of side measurements that could be used to form a triangle are b) 3, 18, 22 and c) 7, 13, 16.