Scale Factor Word Problems

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. It is used to enlarge or reduce figures in geometry.

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 ft².

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. So, if the scale factor is 2, the area is multiplied by 2² = 4.

Front

If a triangle has a base of 5 cm and a height of 4 cm, what is its area?

Back

Area = 1/2 × base × height = 1/2 × 5 cm × 4 cm = 10 cm².

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

If the scale is 1 cm = 10 km, how far apart are two cities that are 15 cm apart on the map?

Back

Actual distance = 15 cm × 10 km/cm = 150 km.

Front

What is the effect of a scale factor of 3 on the area of a square with a side length of 2 m?

Back

New area = (3 × 2 m)² = 6 m² = 36 m².

Front

If a shape is enlarged by a scale factor of 4, what is the new perimeter if the original perimeter is 10 m?

Back

New perimeter = 4 × 10 m = 40 m.

Front

What is the relationship between scale factor and dimensions of a shape?

Back

The dimensions of a shape are multiplied by the scale factor, affecting both perimeter and area.

Front

If a map has a scale of 1 inch = 50 miles, how many miles are represented by 3 inches?

Back

Actual distance = 3 inches × 50 miles/inch = 150 miles.