Question

Which numbers could represent the lengths of a triangle

A.5,9,14
B.7,7,15
C.1,2,4
D.3,6,8

Answer 1

A and D

Explanation:

you would have to test each option using the triangle inequality theorem

which is when the sum of any two sides of the triangle are greater than or equal to the third side

A) 5+9
`\geq` 14 true

5+14
`\geq` 9 true

14+9
`\geq` 5 true

B) 7+7
`\geq` 15 false This answer can be eliminated

C) 1+2
`\geq` 4 false This answer can be eliminated

D) 3+6
`\geq` 9 true

3+8
`\geq` 6 true

6+9
`\geq` 3 true

Answer 2

The lengths of a triangle must satisfy the triangle inequality which states that the sum of any two sides must be greater than the third side.

For option A:

5 + 9 = 14, which satisfies the triangle inequality. However, 5 + 14 = 19, which is not greater than 9. Therefore, this set of numbers does not satisfy the triangle inequality.

For option B:

7 + 7 = 14, which is less than 15. Therefore, this set of numbers does not satisfy the triangle inequality.

For option C:

1 + 2 = 3, which satisfies the triangle inequality. However, 1 + 4 = 5, which is not greater than 2. Therefore, this set of numbers does not satisfy the triangle inequality.

For option D:

3 + 6 = 9, which satisfies the triangle inequality. 3 + 8 = 11 and 6 + 8 = 14, both of which are greater than 8. Therefore, this set of numbers satisfies the triangle inequality.

So, the numbers 3, 6, and 8 could represent the lengths of a triangle. Therefore, the answer is option D.