Proportions and Ratios: Solving Similar Triangle Problems

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

• 25 feet

• 20 feet

• 15 feet

Two similar triangles have sides in the ratio of 2:5. If the shorter triangle has a side measuring 8 cm, what is the length of the corresponding side in the larger triangle?

• 25 cm

• 16 cm

• 12 cm

• 20 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?

• 20 feet

• 40 feet

• 30 feet

• 50 feet

A flagpole is 15 feet tall and casts a shadow of 10 feet. If a nearby building casts a shadow of 50 feet, how tall is the building?

• 100 feet

• 50 feet

• 30 feet

• 75 feet

In a triangle, one angle measures 30 degrees and the corresponding angle in a similar triangle measures 60 degrees. If the shorter triangle has a side of 10 cm, what is the length of the corresponding side in the larger triangle?

• 20 cm

• 15 cm

• 25 cm

• 30 cm

A 3-foot tall statue casts a shadow of 2 feet. If a nearby lamp post casts a shadow of 8 feet, how tall is the lamp post?

• 15 feet

• 10 feet

• 5 feet

• 12 feet

Two similar triangles have a ratio of 3:4. If the perimeter of the smaller triangle is 30 cm, what is the perimeter of the larger triangle?

• 50 cm

• 40 cm

• 35 cm

• 25 cm

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

• 15 feet

• 13.89 feet

• 10 feet

• 12 feet

A rectangular garden is 10 meters long and 6 meters wide. If a similar garden is scaled up by a factor of 2, what will be the area of the larger garden?

• 60 square meters

• 120 square meters

• 240 square meters

• 180 square meters

A 4-inch tall model of a car is similar to the actual car. If the actual car is 16 inches tall, what is the scale factor of the model to the actual car?

• 1/2

• 1/3

• 2/1

• 1/4