Final Answer:
Given AC = 49 cm and AB = 5.2 cm, BC must fall within the range of 43.8 cm < BC < 54.2 cm according to the triangle inequality theorem. The correct option is B: BC = 44.8 cm, as it falls within this range.
Step-by-step explanation:
Given that AC = 49 cm and AB = 5.2 cm in △ABC, 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. Therefore, BC must be such that AC - AB < BC < AC + AB.
Calculating the range for BC:
AC - AB = 49 cm - 5.2 cm = 43.8 cm
AC + AB = 49 cm + 5.2 cm = 54.2 cm
So, BC must fall within the range of 43.8 cm < BC < 54.2 cm. Among the given options, the value closest to this range is BC = 44.8 cm.
In triangle △ABC, we're given the lengths AC = 49 cm and AB = 5.2 cm. To determine the possible range for the length of BC, we employ the triangle inequality theorem. According to this theorem, for any triangle, the length of one side must be less than the sum of the other two sides and greater than their difference. Mathematically, BC must satisfy the inequality AC - AB < BC < AC + AB.
Substituting the given values into the inequality, we obtain the range:
AC - AB = 49 cm - 5.2 cm = 43.8 cm
AC + AB = 49 cm + 5.2 cm = 54.2 cm
Therefore, the possible range for BC is 43.8 cm < BC < 54.2 cm. Among the provided options, the value closest to this range is BC = 44.8 cm. This value satisfies the conditions dictated by the triangle inequality theorem for the given sides AC and AB, making it the most suitable length for BC in this scenario. Hence, option B with BC = 44.8 cm aligns with the principles of the triangle inequality theorem and the given side lengths of the triangle △ABC.correct option is b.