Question

A triangle has two sides of lengths 7 and 12. What value could the length of

the third side be? Check all that apply.
DA. 11
B. 7
☐ C. 17
D. 3
E. 5
F. 9

Answer 1

Answer: 7,11,9

Explanation:

The third side will be 7,11,9

Answer 2

To determine the possible lengths of the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the two sides have lengths 7 and 12. Therefore, the third side must satisfy:

12 - 7 < third side < 12 + 7

5 < third side < 19

Thus, the possible values for the length of the third side are:

A. 11 (satisfies the inequality)
B. 7 (does not satisfy the inequality; the third side must be greater than 5)
C. 17 (satisfies the inequality)
D. 3 (does not satisfy the inequality; the third side must be greater than 5)
E. 5 (does not satisfy the inequality; the third side must be greater than 5)
F. 9 (satisfies the inequality)

Therefore, the correct answers are A, C, and F.