Real-World Triangle Problems: Discovering Similarity

1. A 6-foot tall person casts a shadow of 4 feet. If a nearby tree casts a shadow of 10 feet, how tall is the tree?

• 8 feet

• 15 feet

• 20 feet

• 12 feet

2. Two similar triangles have sides in the ratio of 3:5. If the shorter triangle has a side measuring 9 cm, what is the length of the corresponding side in the larger triangle?

• 15 cm

• 20 cm

• 18 cm

• 12 cm

3. A model of a building is made with a height of 2 meters and a base of 1 meter. If the actual building is 50 meters tall, what is the width of the actual building if the model's width is 0.5 meters?

• 10 meters

• 15 meters

• 8 meters

• 12.5 meters

4. A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 15 feet long and reaches a height of 12 feet on the wall, how far is the base of the ladder from the wall?

• 10 feet

• 8 feet

• 9 feet

• 11 feet

5. In a park, two trees are similar in shape. If the smaller tree is 3 meters tall and the larger tree is 5 meters tall, what is the ratio of their heights?

• 4:3

• 3:2

• 5:3

• 2:1

6. A flagpole casts a shadow of 20 feet long. If a 5-foot tall person casts a shadow of 4 feet, how tall is the flagpole?

• 25 feet

• 10 feet

• 30 feet

• 15 feet

7. A triangular garden has a height of 8 feet and a base of 6 feet. If a similar triangular garden has a base of 12 feet, what is its height?

• 10 feet

• 16 feet

• 12 feet

• 14 feet

8. A 10-foot tall statue casts a shadow of 5 feet. If a nearby building casts a shadow of 25 feet, how tall is the building?

• 50 feet

• 40 feet

• 30 feet

• 60 feet

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

• 30 cm

• 42 cm

• 48 cm

• 36 cm

10. A 4-foot tall child stands next to a similar 6-foot tall adult. If the child casts a shadow of 3 feet, how long is the adult's shadow?

• 2 feet

• 6 feet

• 4.5 feet

• 5 feet