Question

The measures of two sides of a triangle are 7 and 12. Which of the

following is a possible length of the third side of the triangle?
5
6
19
20

Answer 1

The only possible length for the third side of the triangle, given the two sides are 7 and 12, obeying the Triangle Inequality Theorem, is 6.

Step-by-step explanation:

The question asks about determining the possible length of the third side of a triangle when the measures of two sides are known to be 7 and 12. According to the Triangle Inequality Theorem, the lengths of any two sides of a triangle must sum to be greater than the length of the third side. Therefore, we look for a length that, when added to 7 or 12, is greater than the other length but, when subtracted, is less than the other length.

For each option:

1. 5 is not possible because 12 - 7 = 5, which does not satisfy the Triangle Inequality Theorem.
2. 6 is possible because 12 - 7 < 6 and 12 + 7 > 6.
3. 19 is not possible because 12 + 7 is not greater than 19.
4. 20 is not possible because 12 + 7 is not greater than 20.

Therefore, the only possible length of the third side that satisfies the conditions of the Triangle Inequality Theorem is 6.