In triangle ABC, the length of side AB is 10 inches and the length of side BC is 19 inches. Which of the following could be the length of side AC?
7 inches
31 inches
24 inches
34 inches
31
The answer to your question is 23 inches
To determine which of the given lengths could be the length of side AC in triangle ABC, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's go through each option:
1. 7 inches: To verify if 7 inches could be the length of side AC, we check if AB + AC > BC.
10 + 7 > 19
17 > 19
Since 17 is not greater than 19, 7 inches cannot be the length of side AC.
2. 31 inches: To check if 31 inches could be the length of side AC, we use the same inequality.
10 + 31 > 19
41 > 19
31 inches satisfies the triangle inequality theorem, so it is a possible length for side AC.
3. 24 inches: Let's check if 24 inches satisfies the triangle inequality.
10 + 24 > 19
34 > 19
24 inches also satisfies the triangle inequality theorem and can be a possible length for side AC.
4. 34 inches: We will check if 34 inches satisfies the triangle inequality.
10 + 34 > 19
44 > 19
34 inches satisfies the triangle inequality theorem, so it is a possible length for side AC.
Both 31 inches and 34 inches could be the length of side AC in triangle ABC, so the correct answers are:
- 31 inches
- 34 inches
recall that
BC-AB < AC < BC+AB