Question 1: Calculate the length of side AB in a triangle where sides AC = 7 cm, BC = 9 cm, and all sides are of different lengths. Side AB is opposite angle C, which is 60°.

Answer: calculate using Law of Cosines

Question 2: Construct a triangle with sides of lengths 6 cm, 8 cm, and 10 cm. Is it scalene? Explain your reasoning.

Answer: Yes, all sides are different lengths, so it is scalene

Question 3: If a triangle has sides of 5 cm, 7 cm, and 10 cm, determine whether it is scalene. Show your working.

Answer: all sides are different, so scalene

Question 4: Plot the triangle with vertices at (0,0), (4,0), and (2, 3). Does this triangle appear scalene? Justify your answer.

Answer: calculate distances and compare; all sides different

Question 5: In a triangle, sides AB = 8 cm, AC = 6 cm, and BC = 8 cm. Is this triangle scalene? Why or why not?

Answer: No, because two sides are equal (AB and BC), so not scalene

Question 6: Determine the possible range of lengths for side XY in a scalene triangle where sides XZ and YZ are 5 cm and 9 cm respectively.

Answer: greater than 4 cm and less than 14 cm

Question 7: Identify and explain the common mistake made when assuming a triangle with sides 4 cm, 5 cm, and 9 cm is scalene.

Answer: They might overlook that the sum of 4 and 5 equals 9, which violates triangle inequality; thus, not a valid triangle

Question 8: A triangle has sides measuring 10 cm, 12 cm, and 14 cm. Calculate the area using Heron's formula.

Answer: approximate area from Heron's formula

Question 9: Explain why all sides of a scalene triangle must be of different lengths, and give an example of a scalene triangle with sides 3 cm, 4 cm, and 5 cm.

Answer: By definition, scalene triangles have all sides different; example sides: 3, 4, 5

Question 10: Challenge: Find the length of the third side of a triangle when two sides are 7 cm and 10 cm, and the triangle is scalene with an included angle of 45° between these sides.

Answer: calculate using Law of Cosines