To solve this problem, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
Let's check the answer choices using the triangle inequality theorem:
A. 44 inches: AB + BC = 15 + 24 = 39. Since 39 is less than 44, this is not a possible length for side AC.
B. 34 inches: AB + BC = 15 + 24 = 39. Since 39 is greater than 34, this is a possible length for side AC.
C. 41 inches: AB + BC = 15 + 24 = 39. Since 39 is less than 41, this is not a possible length for side AC.
D. 7 inches: AB + BC = 15 + 24 = 39. Since 39 is greater than 7, this is a possible length for side AC.
Therefore, the possible length of side AC is 34 inches (option B) and 7 inches (option D).
In triangle ABC, the length of side AB is 15 inches and the length of side BC is 24 inches. Which of the following could be the length of side AC?
A.
44 inches
B.
34 inches
C.
41 inches
D.
7 inches
1 answer