Proportions in Action: Solving Similar Triangle Problems

A tree casts a shadow of 15 feet. At the same time, a 5-foot tall person casts a shadow of 2 feet. How tall is the tree?

• 50 feet

• 37.5 feet

• 25 feet

• 10 feet

Two similar triangles have a ratio of their sides of 3:5. If the shorter triangle has a base of 9 cm, what is the length of the base of the larger triangle?

• 15 cm

• 12 cm

• 20 cm

• 18 cm

A model of a building is made with a height of 4 feet and a width of 2 feet. If the actual building is 60 feet tall, how wide is the actual building?

• 50 feet

• 30 feet

• 20 feet

• 40 feet

A 10-foot tall flagpole casts a shadow of 8 feet. How long is the shadow of a 5-foot tall person standing nearby?

• 10 feet

• 2 feet

• 4 feet

• 6 feet

In a park, two similar triangular flower beds have a ratio 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

A 12-foot ladder reaches a wall at a height of 9 feet. If another ladder is 16 feet long, how high will it reach on the same wall?

• 10 feet

• 15 feet

• 12 feet

• 13.89 feet

A photograph of a building is taken from a distance, creating a triangle with a height of 3 inches and a base of 4 inches. If the actual building is 60 feet tall, how far away is the photographer standing?

• 80 feet

• 100 feet

• 20 feet

• 40 feet

Two similar triangles have perimeters of 24 cm and 36 cm. If the shorter triangle has a side length of 4 cm, what is the corresponding side length of the larger triangle?

• 8 cm

• 7 cm

• 6 cm

• 5 cm

A 5-foot tall person is standing next to a similar 8-foot tall person. If the shorter person casts a shadow of 3 feet, how long is the shadow of the taller person?

• 7 feet

• 4.8 feet

• 6 feet

• 5 feet

A triangular park has a height of 30 meters and a base of 20 meters. If a similar triangular park has a base of 50 meters, what is the height of the larger park?

• 75 meters

• 60 meters

• 90 meters

• 100 meters