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 the proportional relationship between two similar figures.

Front

How do you calculate the actual distance using a map scale?

Back

To find the actual distance, multiply the distance on the map by the scale factor. For example, if the scale is 2 inches = 40 miles and the distance on the map is 4.125 inches, the actual distance is 4.125 * (40/2) = 82.5 miles.

Front

If a rectangle's side lengths are multiplied by a scale factor of 2, how do you find the new area?

Back

The new area can be found by squaring the scale factor and multiplying it by the original area. If the original area is A, the new area is A * (scale factor)^2.

Front

What is the formula to convert map distance to actual distance?

Back

Actual Distance = Map Distance × (Actual Distance per Unit of Map Distance). For example, if the scale is 1 cm = 8 km and the map distance is 24 cm, the actual distance is 24 × 8 = 192 km.

Front

What does a scale of 1 cm = 4 ft mean?

Back

It means that every 1 centimeter on the drawing or map represents 4 feet in reality.

Front

How do you find the actual length of an object from a scale drawing?

Back

Multiply the length of the object in the scale drawing by the scale factor. For example, if a car is 3 cm long in a scale drawing with a scale of 1 cm = 4 ft, the actual length is 3 × 4 = 12 feet.

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 the original area multiplied by k^2.

Front

If two similar figures have a scale factor of 3, how does this affect their perimeters?

Back

The perimeter of the larger figure will be 3 times the perimeter of the smaller figure.

Front

What is the actual distance if the map distance is 10 inches and the scale is 1 inch = 20 miles?

Back

Actual Distance = 10 inches × 20 miles/inch = 200 miles.

Front

How do you convert a scale drawing measurement to actual size?

Back

Use the scale to convert the measurement. For example, if the scale is 1 cm = 5 m and the drawing measures 6 cm, the actual size is 6 cm × 5 m/cm = 30 m.