Question 1: A triangle has side lengths of 7 cm, 9 cm, and 11 cm. Is this triangle scalene? Justify your answer.

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

Question 2: Calculate the perimeter of a scalene triangle with sides of 8 cm, 15 cm, and 20 cm.

Answer: 43

Question 3: Construct a scalene triangle with side lengths of 6 cm, 10 cm, and 14 cm. Use the grid to draw it accurately.

Answer: Drawn on grid with specified lengths.

Question 4: If one side of a scalene triangle measures 12 cm and the other two sides are 9 cm and 15 cm, is the triangle possible? Explain why or why not.

Answer: Yes, because the sum of any two sides exceeds the third in all cases.

Question 5: Find the length of the third side of a triangle if two sides are 10 cm and 13 cm, and the triangle is scalene. The third side is longer than 8 cm but less than 15 cm.

Answer: Between 8 and 15, not equal to 10 or 13

Question 6: Calculate the area of a scalene triangle with base 9 cm and height 12 cm.

Answer: 54

Question 7: A ladder leans against a wall, forming a scalene triangle with the ground and wall. The ladder is 13 meters long, the wall height is 5 meters, and the distance from the wall to the ladder's base is 8 meters. Verify whether the triangle is scalene based on these lengths.

Answer: Yes, all sides are different lengths, so the triangle is scalene.

Question 8: Given two sides of a scalene triangle are 7 cm and 10 cm, what is the range of possible lengths for the third side?

Answer: 3 cm to 17 cm, excluding 7 and 10

Question 9: A surveyor measures three different distances to form a triangle: 25 m, 30 m, and 45 m. Determine if this triangle can be scalene.

Answer: Yes, all sides are different, satisfying scalene conditions.

Question 10: Identify the common mistake students make when assuming a triangle with sides 5 cm, 5 cm, and 8 cm is scalene. Correct the mistake.

Answer: They incorrectly think sides must all be different; but since two sides are equal, the triangle isn't scalene. The correct classification is isosceles.

Question 11: Challenge: Find all possible integer lengths for the third side of a scalene triangle if the other two sides are 9 cm and 14 cm.

Answer: 10 cm, 11 cm, 12 cm, 13 cm (excluding 9 and 14)