Question 1: If a triangle has sides measuring 12 cm, 15 cm, and 18 cm, and it is reduced by a scale factor of 2/3, what are the lengths of the sides of the reduced triangle? Show your working.

Answer: 8 cm, 10 cm, 12 cm

Question 2: Construct a triangle similar to one with sides 10 cm, 14 cm, and 18 cm, scaled down by a factor of 3/4. Use the grid to draw the new triangle.

Answer: See diagram on response area

Question 3: A rectangle measures 24 cm by 36 cm. It is reduced by a scale factor of 1/2. What is the area of the reduced rectangle? Show your working.

Answer: 216 cm²

Question 4: A map shows a park that is 120 meters long. If the map uses a reduction scale factor of 1/10, what is the actual length of the park? Show your working.

Answer: 12 meters

Question 5: A square with side length 16 cm is reduced by a scale factor of 3/8. What is the side length of the reduced square? Show your working.

Answer: 6 cm

Question 6: A photograph measures 30 cm by 20 cm. It is reduced to a size where each dimension is 3/4 of its original length. What are the new dimensions? Show your working.

Answer: 22.5 cm by 15 cm

Question 7: A pair of similar triangles has sides 9 cm, 12 cm, and 15 cm. The larger triangle is scaled down to produce the smaller triangle. Find the scale factor if the smallest side of the smaller triangle measures 6 cm.

Answer: 1/2

Question 8: A poster measures 80 cm by 120 cm. It is reduced by a scale factor of 2/5. What are the dimensions of the reduced poster? Show your working.

Answer: 32 cm by 48 cm

Question 9: A rectangular garden is 15 meters long and 10 meters wide. It is scaled down to a model with a scale factor of 1/3. What are the model's dimensions?

Answer: 5 meters by 3.33 meters

Question 10: Identify and correct the mistake in this reduction: A figure with sides 18 cm, 24 cm, and 30 cm was scaled down by a factor of 2/3, resulting in sides 12 cm, 16 cm, and 20 cm.

Answer: The third side should be 20 cm, not 20 cm (correct calculation: 30 × 2/3 = 20 cm)