Solving Real-World Problems with Similar Triangles

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

A model of a building is made to a scale of 1:100. If the model is 2 meters tall, how tall is the actual building?

• 150 meters

• 50 meters

• 200 meters

• 300 meters

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

A 6-foot tall person is standing 10 feet away from a wall. If the top of their head is 1 foot below the top of the wall, how tall is the wall?

• 6 feet

• 7 feet

• 8 feet

• 5 feet

A flagpole is 20 feet tall and casts a shadow of 10 feet. If a nearby tree casts a shadow of 15 feet, how tall is the tree?

• 40 feet

• 30 feet

• 25 feet

• 35 feet

A triangular park has a height of 12 meters and a base of 16 meters. If a similar triangular park has a base of 24 meters, what is its height?

• 15 meters

• 20 meters

• 10 meters

• 18 meters

A 4-foot tall statue casts a shadow of 3 feet. If a nearby building casts a shadow of 30 feet, how tall is the building?

• 35 feet

• 25 feet

• 40 feet

• 20 feet

A scale drawing of a triangular garden shows one side as 5 inches. If the actual garden is 20 feet long, what is the scale of the drawing?

• 1:48

• 1:60

• 1:36

• 1:24

Two similar triangles have a ratio of 2:3. If the area of the smaller triangle is 50 square meters, what is the area of the larger triangle?

• 112.5 square meters

• 75 square meters

• 90 square meters

• 100 square meters

A 10-foot tall lamppost casts a shadow of 5 feet. If a nearby tree casts a shadow of 15 feet, how tall is the tree?

• 20 feet

• 25 feet

• 10 feet

• 30 feet