Measuring Similar Figures: Ratios and Indirect Sizing

1. A rectangle has a length of 8 cm and a width of 4 cm. If a similar rectangle has a length of 12 cm, what is its width?

• 7 cm

• 5 cm

• 9 cm

• 6 cm

2. Two similar triangles have a ratio of 3:5. If the perimeter of the smaller triangle is 24 cm, what is the perimeter of the larger triangle?

• 30 cm

• 50 cm

• 36 cm

• 40 cm

3. A model of a building is 2 meters tall and the actual building is 10 meters tall. If the model's base is 0.5 meters wide, how wide is the actual building's base?

• 4.0 meters

• 1.5 meters

• 3.0 meters

• 2.5 meters

4. A square garden has an area of 64 square meters. If a similar square garden has a side length of 12 meters, what is the area of the larger garden?

• 100 square meters

• 80 square meters

• 144 square meters

• 64 square meters

5. Two similar trapezoids have a ratio of 1:4. If the area of the smaller trapezoid is 10 square meters, what is the area of the larger trapezoid?

• 160 square meters

• 100 square meters

• 40 square meters

• 80 square meters

6. A triangle has a base of 6 cm and a height of 4 cm. If a similar triangle has a height of 10 cm, what is the length of its base?

• 20 cm

• 15 cm

• 12 cm

• 8 cm

7. A rectangular swimming pool is 15 meters long and 10 meters wide. If a similar pool is 25 meters long, what is its width?

• 20 meters

• 12 meters

• 16.67 meters

• 18 meters

8. A small park is shaped like a rectangle with a length of 20 meters and a width of 10 meters. If a similar park is 3 times larger in both dimensions, what is the area of the larger park?

• 1800 square meters

• 400 square meters

• 600 square meters

• 1000 square meters

9. Two similar figures have a ratio of 2:3. If the area of the smaller figure is 18 square meters, what is the area of the larger figure?

• 36 square meters

• 27 square meters

• 54 square meters

• 40.5 square meters

10. A shadow of a tree is 4 meters long, and the tree is 10 meters tall. If a nearby pole casts a shadow of 2 meters, how tall is the pole?

• 7 meters

• 8 meters

• 5 meters

• 3 meters