Question

Given the following lengths, which lengths are possible for a triangle to have?

A)7, 10, 18
B)2, 6, 9
С)13, 15, 24
D)100, 100, 200

Answer 1

To determine which lengths are possible for a triangle, check if the sum of any two sides is greater than the third side. The possible triangles are A) 7, 10, 18 and C) 13, 15, 24.

Step-by-step explanation:

A triangle can only be formed if the sum of the lengths of any two sides is greater than the length of the third side. Let's check each set of lengths:

1. A) 7, 10, 18: Since 7+10 is greater than 18 and 7+18 is also greater than 10, this is a possible triangle.
2. B) 2, 6, 9: 2+6 is only equal to 8 which is not greater than 9. So, this is not a possible triangle.
3. C) 13, 15, 24: 13+15 is greater than 24 and 13+24 is also greater than 15, so this is a possible triangle.
4. D) 100, 100, 200: 100+100 is equal to 200, but it is not greater than 200. So, this is not a possible triangle.

Therefore, the possible triangles are A) 7, 10, 18 and C) 13, 15, 24.