Similar Triangles: Ratios and Shadow Problems for 7th Grade

A tree casts a shadow of 15 feet. At the same time, a 6-foot tall person casts a shadow of 3 feet. Are the triangles formed by the tree and its shadow similar to the triangles formed by the person and their shadow?

• Yes, the triangles are similar.

• The triangles are similar only if the tree is taller.

• No, the triangles are not similar.

• The triangles are similar only if the shadows are equal in length.

If two similar triangles have a ratio of 2:3, and the shorter side of the first triangle is 4 cm, what is the length of the corresponding side in the second triangle?

• 8 cm

• 7 cm

• 6 cm

• 5 cm

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

• 1/20

• 1/5

• 1/15

• 1/10

In a park, a 10-foot tall flagpole casts a shadow of 5 feet. If a nearby statue casts a shadow of 2 feet, how tall is the statue?

• 4 feet

• 6 feet

• 3 feet

• 5 feet

Two similar triangles have side lengths in the 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?

• 15 cm

• 20 cm

• 25 cm

• 10 cm

A ladder leans against a wall, forming a right triangle. If the ladder is 12 feet long and reaches a height of 9 feet, what is the length of the shadow cast by the ladder on the ground?

• 7.94 feet

• 5.5 feet

• 10 feet

• 8.5 feet

A 4-foot tall plant casts a shadow of 2 feet. If a nearby tree casts a shadow of 10 feet, how tall is the tree?

• 30 feet

• 20 feet

• 5 feet

• 15 feet

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

• The triangles are similar.

• The triangles cannot be compared.

• The triangles are congruent.

• The triangles have different side lengths.

A 5-foot tall person stands next to a similar triangle formed by a 15-foot tall building. If the person's shadow is 2 feet long, how long is the shadow of the building?

• 10 feet

• 4 feet

• 6 feet

• 8 feet

Two similar triangles have a perimeter of 24 cm for the smaller triangle and a perimeter of 36 cm for the larger triangle. What is the ratio of their corresponding side lengths?

• 1:2

• 2:3

• 4:5

• 3:4