Question 1: A scalene triangle has sides measuring 7 cm, 9 cm, and 12 cm. Calculate its perimeter.

Answer: 28

Question 2: In a scalene triangle, if two sides are 8 cm and 15 cm, what is the range of possible lengths for the third side?

Answer: 7 < third side < 23

Question 3: Construct a scalene triangle with sides measuring 5 cm, 9 cm, and 11 cm. Use the grid to draw it accurately.

Answer: Constructed triangle with given side lengths

Question 4: Explain why all sides in a scalene triangle are of different lengths. Use a brief reasoning.

Answer: In a scalene triangle, no sides are equal, so each side must be of a different length to satisfy the definition.

Question 5: Calculate the area of a scalene triangle with base 10 cm and height 6 cm.

Answer: 30

Question 6: A triangle has sides measuring 6 cm, 8 cm, and 10 cm. Verify if it is scalene and justify your answer.

Answer: Yes, all sides are of different lengths: 6, 8, and 10 cm.

Question 7: Plot the graph of y = 2x for x values from -3 to 3. Use the grid.

Answer: Line passing through points (-3,-6), (0,0), (3,6)

Question 8: Construct a scalene triangle with one side 7 cm and two other sides measuring 10 cm and 12 cm. Use the grid.

Answer: Constructed triangle with specified sides

Question 9: Identify a common mistake students make when assuming all triangles with different sides are scalene. Describe and correct it.

Answer: Mistake: Assuming all triangles with different sides are scalene. Correction: Only triangles with all sides of different lengths are scalene; some may be isosceles or equilateral.

Question 10: A triangle has sides measuring 5 cm, 5 cm, and 8 cm. Is it scalene? Explain why or why not.

Answer: No, because two sides are equal (5 cm and 5 cm), so it is isosceles, not scalene.

Question 11: A scalene triangle has sides 9 cm, 14 cm, and 20 cm. Calculate the semi-perimeter and then find the area using Heron's formula.

Answer: Semi-perimeter = 21.5 cm; Area ≈ 84.6 cm²