Scale Factors and Ratios in Geometry

This video tutorial covers Math 7 Unit 4 Lesson 1, focusing on proportional relationships and percentages. It introduces the concept of scale factors and explores how geometric shapes can be scaled versions of each other. The lesson includes practical examples using the dimensions of the US flag and scale models, providing calculations for areas and percentages. The video concludes with practice problems and homework assignments to reinforce the concepts learned.

Which of the following pairs of shapes are scaled versions of each other?

• A square with side 5 and a square with side 3

• A triangle with base 3 and height 4, and a triangle with base 6 and height 8

• A rectangle with dimensions 2x4 and a rectangle with dimensions 3x6

• A circle with radius 4 and a circle with radius 6

What is a scale factor?

• A number used to increase the size of an object

• A number used to decrease the size of an object

• A number used to multiply each dimension of an object to create a scaled version

• A number used to divide each dimension of an object to create a scaled version

If a classroom flag is a quarter the size of a standard 19x10 ft flag, what would be the dimensions of the classroom flag?

• 9.5 ft by 5 ft

• 4.75 ft by 2.5 ft

• 19 ft by 10 ft

• 2.375 ft by 1.25 ft

What percentage of the US flag is taken up by the union?

• 15%

• 25%

• 22%

• 30%

How many red stripes are there on the US flag?

• 9

• 6

• 7

• 8

What is the ratio of the largest flag in the world compared to the official government flag ratio?

• 1:1.9

• 1:1.5

• 1:2

• 1:2.24

If a scale model of a train is created with a scale of 1:48, what is the actual height of the train if the model is 102 mm?

• 4896 mm

• 204 mm

• 489.6 mm

• 102 mm

Can a modern train with a scale of 1:48 fit on old tracks that are 4.5 ft apart?

• No, the train is too narrow

• Yes, but only with modifications

• No, the train is too wide

• Yes, it fits perfectly

What is the conversion factor from millimeters to meters?

• 1 meter = 100 mm

• 1 meter = 10 mm

• 1 meter = 500 mm

• 1 meter = 1000 mm

If a rectangle has a height to width ratio of 3:4.5, what would be the dimensions if scaled by a factor of 2?

• 1.5:2.25

• 3:4.5

• 6:9

• 9:13.5