Proportions and Scale Factors in Similar Triangles

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

• 10 feet

• 15 feet

• 25 feet

• 20 feet

Two similar triangles have a scale factor of 2. If the shorter triangle has a base of 4 cm, what is the base of the larger triangle?

• 12 cm

• 10 cm

• 8 cm

• 6 cm

A model of a building is 1/100th the size of the actual building. If the model is 2 meters tall, how tall is the actual building?

• 50 meters

• 150 meters

• 200 meters

• 100 meters

A 6-foot tall flagpole casts a shadow of 8 feet. If a nearby building casts a shadow of 32 feet, how tall is the building?

• 16 feet

• 30 feet

• 24 feet

• 20 feet

In a triangle, if the lengths of two sides are 3 cm and 4 cm, and the scale factor to a similar triangle is 3, what are the lengths of the corresponding sides in the larger triangle?

• 12 cm and 15 cm

• 6 cm and 8 cm

• 9 cm and 12 cm

• 7 cm and 10 cm

A photograph of a person is 10 inches tall and the actual person is 5 feet tall. What is the scale factor of the photograph to the actual person?

• 1/8

• 1/4

• 1/6

• 1/5

Two similar triangles have corresponding sides of lengths 8 cm and 12 cm. If the shorter triangle has a height of 5 cm, what is the height of the larger triangle?

• 8 cm

• 7.5 cm

• 10 cm

• 6 cm

A 4-foot tall statue casts a shadow of 6 feet. If a nearby lamp post casts a shadow of 18 feet, how tall is the lamp post?

• 12 feet

• 8 feet

• 10 feet

• 15 feet

A rectangular garden is 10 meters long and 5 meters wide. If a similar garden is scaled up by a factor of 2, what will be the dimensions of the larger garden?

• 25 meters long and 12.5 meters wide

• 20 meters long and 10 meters wide

• 10 meters long and 5 meters wide

• 15 meters long and 7.5 meters wide

If two similar triangles have a ratio of 3:5, and the shorter triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle?

• 30 cm

• 50 cm

• 36 cm

• 40 cm