Similar Triangles Area and Perimeter

A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 21 feet. How tall is the building? (Draw a picture, set up a proportion)

• 16 feet

• 21 feet

• 24 feet

• 28 feet

Identify the perimeter and area ratios for the following figures.

• Per. Ratio=8  Area Ratio=64

• Per. Ratio=8/48  Area Ratio=64/2304

• Per. Ratio=8/48  Area Ratio=8/48

• Per. Ratio=8/48  Area Ratio=2304/64

All corresponding sides are proportional (same ratio) in similar figures.

• True

• False

Are the triangles similar? If so, what similarity shortcut is used? Show all work.

• Similar.  SSS

• Similar.  SAS

• Similar.  AA

• Not Similar.

Two sides of an isosceles triangle are 10 inches and 20 inches.  If the shortest side of a similar triangle is 50 inches, what is the perimeter of the larger triangle?

• 250"

• 200"

• 150"

• 100"

The ratio of the areas of two similar triangles is 4:9. What is the ratio of the perimeters?

• 4:9

• 2:3

• 16:81

• 9:4

The length of the sides of two similar triangles are in the ratio of 2:3. If the area of the larger triangle is 45 cm², find the area of the smallest triangle.

• 30 cm²

• 15 cm²

• 10 cm²

• 20 cm²

If BD=16, AC=10 and DE=3, what is the perimeter of triangle ABC (add all sides of big triangle)

• 48

• 16

• 27

• 29

The ratio of the sides of two similar triangles is 5:6. If the area of the smaller triangle is 50 km², what is the area of the larger triangle?

• 60 km²

• 72 km²

• 34.7 km²

• 42.7 km²

∆ABC∼∆XYZ. If the perimeter of ∆ABC is 36, the perimeter of ∆XYZ is 9, and AB=12 what is the length of XY?

• 3

• 1.33

• 48

• 192