Proportions & Theorems: Uncovering 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?

• 37.5 feet

• 25 feet

• 50 feet

• 10 feet

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?

• 18 cm

• 12 cm

• 20 cm

• 15 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?

• 40 feet

• 50 feet

• 30 feet

• 20 feet

A 10-foot ladder reaches a wall at a height of 8 feet. If the ladder is moved back, forming a similar triangle, how far is the base of the ladder from the wall?

• 6 feet

• 4 feet

• 10 feet

• 8 feet

In a park, two trees are similar in shape. If the smaller tree is 3 meters tall and the larger tree is 5 meters tall, what is the ratio of their heights?

• 4:3

• 5:3

• 2:1

• 3:5

A flagpole is 12 feet tall and casts a shadow of 8 feet. A nearby building casts a shadow of 40 feet. How tall is the building?

• 24 feet

• 60 feet

• 36 feet

• 48 feet

A triangle has sides measuring 6 cm, 8 cm, and 10 cm. If a similar triangle has its longest side measuring 15 cm, what are the lengths of the other two sides?

• 9 cm, 12 cm

• 7 cm, 14 cm

• 8 cm, 16 cm

• 10 cm, 15 cm

A 4-foot tall statue casts a shadow of 2 feet. If a nearby building casts a shadow of 30 feet, how tall is the building?

• 90 feet

• 45 feet

• 60 feet

• 75 feet

Two similar triangles have a ratio of 1:4. If the perimeter of the smaller triangle is 12 cm, what is the perimeter of the larger triangle?

• 48 cm

• 60 cm

• 36 cm

• 24 cm

A 5-foot tall person stands 3 feet away from a wall and casts a shadow of 2 feet. If the wall is 10 feet tall, how far is the wall from the person?

• 5 feet

• 8 feet

• 7 feet

• 10 feet