Finding Heights: Similar Triangles and Proportions Quiz

1. A 5-foot tall person casts a shadow of 3 feet. If a nearby tree casts a shadow of 12 feet, how tall is the tree?

• 15 feet

• 20 feet

• 25 feet

• 10 feet

2. Two similar triangles have side lengths in the ratio of 2:3. If one side of the smaller triangle is 8 cm, what is the length of the corresponding side in the larger triangle?

• 14 cm

• 16 cm

• 10 cm

• 12 cm

3. A model of a building is made with a height of 4 feet and a base of 2 feet. If the actual building has a height of 60 feet, what is the width of the actual building?

• 30 feet

• 20 feet

• 40 feet

• 50 feet

4. A flagpole is 15 feet tall and casts a shadow of 10 feet. If a nearby lamppost casts a shadow of 5 feet, how tall is the lamppost?

• 12 feet

• 7.5 feet

• 5 feet

• 10 feet

5. In a park, two similar triangular flower beds have a ratio of their sides of 1:4. If the area of the smaller flower bed is 10 square meters, what is the area of the larger flower bed?

• 80 square meters

• 100 square meters

• 160 square meters

• 40 square meters

6. A 6-foot tall person stands next to a 9-foot tall statue. If the person casts a shadow of 4 feet, how long is the shadow of the statue?

• 10 feet

• 8 feet

• 5 feet

• 6 feet

7. A triangular sail on a boat has a height of 3 meters and a base of 4 meters. If a similar triangular sail has a height of 9 meters, what is the length of its base?

• 10 meters

• 6 meters

• 12 meters

• 8 meters

8. A 10-foot tall tree casts a shadow of 15 feet. If a nearby building casts a shadow of 30 feet, how tall is the building?

• 25 feet

• 20 feet

• 15 feet

• 35 feet

9. Two similar triangles have a side length ratio of 5:7. If the shorter triangle has a side measuring 10 cm, what is the length of the corresponding side in the larger triangle?

• 14 cm

• 18 cm

• 12 cm

• 16 cm

10. A 12-foot tall lighthouse casts a shadow of 8 feet. If a boat mast casts a shadow of 4 feet, how tall is the mast?

• 8 feet

• 4 feet

• 6 feet

• 10 feet