Finding Heights: Calculate Side Lengths in Similar Triangles

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

• 20 feet

• 15 feet

• 25 feet

• 10 feet

Two similar triangles have side lengths in the ratio of 2:3. If the shorter triangle has a side length of 8 cm, what is the corresponding side length in the larger triangle?

• 12 cm

• 14 cm

• 16 cm

• 10 cm

In a park, a 4-foot tall statue casts a shadow of 6 feet. If a nearby lamp post casts a shadow of 15 feet, how tall is the lamp post?

• 8 feet

• 12 feet

• 10 feet

• 14 feet

Two similar triangles have a ratio of 1:4. If one side of the smaller triangle is 5 cm, what is the length of the corresponding side in the larger triangle?

• 20 cm

• 15 cm

• 10 cm

• 25 cm

A 10-foot tall flagpole casts a shadow of 5 feet. If a nearby building casts a shadow of 20 feet, how tall is the building?

• 15 feet

• 10 feet

• 40 feet

• 25 feet

A triangle has sides measuring 6 cm, 8 cm, and 10 cm. A similar triangle has a side measuring 12 cm. What is the length of the corresponding side that measures 8 cm in the larger triangle?

• 14 cm

• 18 cm

• 16 cm

• 10 cm

In a triangle, if one angle measures 30 degrees and the corresponding angle in a similar triangle measures 30 degrees, what can you conclude about the triangles?

• The triangles are similar.

• The triangles are not similar.

• The triangles are congruent.

• The triangles have different angles.

A 3-foot tall child casts a shadow of 2 feet. If a tree casts a shadow of 10 feet, how tall is the tree?

• 5 feet

• 8 feet

• 15 feet

• 12 feet

Two similar triangles have a side length ratio of 5:7. If the shorter triangle has a side measuring 15 cm, what is the length of the corresponding side in the larger triangle?

• 18 cm

• 21 cm

• 25 cm

• 30 cm