Mastering Similar Triangles: Real-World Problem Solving

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?

• 15 feet

• 25 feet

• 20 feet

• 10 feet

Two similar triangles have sides in the ratio of 2:3. If the shorter triangle has a side measuring 4 cm, what is the length of the corresponding side in the larger triangle?

• 8 cm

• 7 cm

• 6 cm

• 5 cm

A model of a building is made using similar triangles. If the model is 2 feet tall and the actual building is 30 feet tall, what is the scale factor of the model to the actual building?

• 1/10

• 1/20

• 1/15

• 1/5

A ladder leans against a wall, forming a right triangle. If the ladder is 10 feet long and reaches 8 feet up the wall, how far is the base of the ladder from the wall?

• 6 feet

• 10 feet

• 8 feet

• 4 feet

In a park, two trees are similar in shape. If the smaller tree is 3 meters tall and the larger tree is 7.5 meters tall, what is the ratio of their heights?

• 3:1

• 2:1

• 4:3

• 5:2

A triangular garden is similar to another garden. If the area of the smaller garden is 50 square meters and the area of the larger garden is 200 square meters, what is the ratio of their corresponding sides?

• 1:3

• 1:2

• 2:3

• 3:4

A flagpole casts a shadow of 15 feet. A nearby building casts a shadow of 45 feet. If the flagpole is 10 feet tall, how tall is the building?

• 35 feet

• 30 feet

• 25 feet

• 20 feet

Two similar triangles have a perimeter of 24 cm for the smaller triangle and 36 cm for the larger triangle. What is the ratio of the perimeters of the two triangles?

• 1:2

• 3:4

• 4:5

• 2:3

A photographer uses a camera to capture a picture of a mountain. If the height of the mountain is 200 meters and the height of the camera from the ground is 2 meters, what is the ratio of the mountain's height to the camera's height?

• 100:1

• 200:1

• 50:1

• 10:1

A rectangular swimming pool is similar to a smaller pool. If the dimensions of the smaller pool are 4 meters by 6 meters, and the length of the larger pool is 12 meters, what is the width of the larger pool?

• 8 meters

• 10 meters

• 6 meters

• 4 meters