Scale Factor Word Problems

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In geometry, it is used to determine how much larger or smaller a figure is compared to the original.

Front

How do you calculate the scale used in a map?

Back

To calculate the scale, divide the actual distance by the distance on the map. For example, if 5 inches on the map represents 210 miles, the scale is 210 miles / 5 inches = 42 miles per inch.

Front

If a rectangle has a length of 4 ft and a width of 3 ft, what is its area?

Back

Area = length × width = 4 ft × 3 ft = 12 square feet.

Front

What happens to the area of a shape when the side lengths are multiplied by a scale factor of 2?

Back

The area is multiplied by the square of the scale factor. If the scale factor is 2, the new area is 2² = 4 times the original area.

Front

What is a scale drawing?

Back

A scale drawing is a representation of an object that is enlarged or reduced in size, maintaining the proportions of the original object.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what are the lengths of the sides if the scale factor is 3?

Back

The new side lengths would be 9 cm, 12 cm, and 15 cm.

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

If the area of a rectangle is 48 square feet and the length is 8 feet, what is the width?

Back

Width = Area / Length = 48 sq ft / 8 ft = 6 ft.

Front

What is the relationship between scale factor and area?

Back

The area of a shape changes by the square of the scale factor. If the scale factor is k, the new area is k² times the original area.

Front

How do you find the new area of a rectangle when each side is multiplied by a scale factor of 3?

Back

If the original area is A, the new area will be 3² × A = 9A.