Mastering Similar Figures: Area and Ratio Challenges

A rectangle has a length of 8 cm and a width of 4 cm. If a similar rectangle has a length of 12 cm, what is its width?

• 7 cm

• 6 cm

• 8 cm

• 5 cm

Two triangles are similar. The first triangle has a base of 6 cm and a height of 3 cm. If the second triangle has a base of 9 cm, what is its height?

• 5 cm

• 6 cm

• 3 cm

• 4.5 cm

A model of a car is 15 inches long and 6 inches wide. If the actual car is 30 inches long, how wide is the actual car?

• 8 inches

• 14 inches

• 12 inches

• 10 inches

A small park is shaped like a rectangle with dimensions 20 m by 10 m. A larger park is similar to the small park and has a length of 30 m. What is the width of the larger park?

• 20 m

• 15 m

• 10 m

• 25 m

Two similar pentagons have a ratio of 2:3. If the area of the smaller pentagon is 50 cm², what is the area of the larger pentagon?

• 112.5 cm²

• 90 cm²

• 100 cm²

• 75 cm²

A square garden has a side length of 5 m. If a similar square garden has a side length of 10 m, how many times larger is the area of the larger garden compared to the smaller one?

• 2

• 4

• 8

• 6

A photograph is 4 inches wide and 6 inches tall. If a similar photograph is 10 inches wide, what is its height?

• 15 inches

• 18 inches

• 8 inches

• 12 inches

A triangle has sides measuring 3 cm, 4 cm, and 5 cm. A similar triangle has a longest side of 10 cm. What are the lengths of the other two sides?

• 5 cm, 7 cm

• 9 cm, 12 cm

• 4 cm, 6 cm

• 6 cm, 8 cm

A blueprint of a house is drawn at a scale of 1:100. If the width of the blueprint is 2 m, what is the actual width of the house?

• 50 m

• 100 m

• 150 m

• 200 m

Two similar circles have a radius ratio of 1:4. If the radius of the smaller circle is 2 cm, what is the radius of the larger circle?

• 4 cm

• 6 cm

• 10 cm

• 8 cm