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Question
Two side lengths of a triangle are shown above. What could be the measurement of the missing side length? (choose 2)
Responses
A14.6 cm
14.6 cm
B22.4 cm
22.4 cm
C20.3 cm
20.3 cm
D25 cm
25 cm
E2.6 cm
Based on the given side lengths, we can use the triangle inequality theorem to determine the possible range of the missing side length.
According to the triangle inequality theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's consider the given side lengths:
Side AB = 8.7 cm
Side BC = 12.9 cm
Using the triangle inequality theorem, we can determine the range of the possible lengths for the missing side AC.
- To find the minimum possible length, we need to subtract the side BC from the side AB:
8.7 cm - 12.9 cm = -4.2 cm
Since a side length cannot be negative, -4.2 cm is not a valid option. Thus, we can eliminate any answer choice below 0 cm.
- To find the maximum possible length, we need to add the side BC to the side AB:
8.7 cm + 12.9 cm = 21.6 cm
Therefore, the possible range for the missing side length AC is from 0 cm to 21.6 cm.
From the given answer choices, the two possible measurements for the missing side length are:
A) 14.6 cm
C) 20.3 cm
Therefore, the correct choices are A14.6 cm and C20.3 cm.