Understanding Ratios in Similar Rectangles

The video tutorial explains how to determine the area of a larger rectangle given the area of a smaller rectangle and the ratio of their perimeters. It covers the relationship between the ratios of perimeters and areas of similar polygons, using squares to illustrate these concepts. The tutorial demonstrates how to calculate the perimeters and areas of squares to verify the given ratios and solve for the unknown area of the larger rectangle using proportional reasoning.

What is the given ratio of the perimeters of the two similar rectangles?

• 3 to 5

• 4 to 5

• 5 to 7

• 2 to 3

If the ratio of the sides of two similar polygons is a to b, what is the ratio of their areas?

• a to b

• a squared to b squared

• a cubed to b cubed

• a to b squared

What is the ratio of the areas of the two squares used in the example?

• 3 to 5

• 9 to 25

• 12 to 20

• 25 to 9

How do you simplify the ratio 12 to 20?

• Divide both by 5

• Divide both by 3

• Divide both by 2

• Divide both by 4

What is the area of the small square in the example?

• 15 square units

• 12 square units

• 9 square units

• 6 square units

What is the area of the large square in the example?

• 35 square units

• 30 square units

• 20 square units

• 25 square units

What is the ratio of the areas of the small and large rectangles?

• 3 to 5

• 12 to 20

• 25 to 36

• 9 to 25

If the area of the small rectangle is 36 square feet, what is the area of the large rectangle?

• 81 square feet

• 121 square feet

• 64 square feet

• 100 square feet

What mathematical operation is used to find the area of the larger rectangle from the smaller one?

• Division

• Addition

• Subtraction

• Multiplication

What is the final answer for the area of the larger rectangle?

• 64 square feet

• 81 square feet

• 121 square feet

• 100 square feet