Cottage A and Cottage B are 8 km apart. Cottage B and Cottage C are 3 km apart. What could be the possible distance/s between cottage A and Cottage C?I. 12kmII. 11kmIII. 8km
Correct answer: D. II and III only
- A. I only
- B. II only
- C. I and II only
- D. II and III only
Explanation
To determine the possible distances between Cottage A and Cottage C, apply the triangle inequality theorem. The sum of any two sides of a triangle must be greater than the length of the remaining side. Considering the sides as 8 km, 3 km, and the unknown distance AC:For 12 km, 8 + 3 = 11, which is less than 12, making this distance not possible.For 11 km, 8 + 3 = 11, which is equal, thus a possible distance.For 8 km, 8 + 3 = 11, which is greater, hence a possible distance.Therefore, the valid distances are 11 km and 8 km, making option D (II and III only) the correct answer.
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