Question

A toy train set includes a train station building which is a scale model of a real building. The area of the front side of the toy building is 1 square foot. The real building’s front side has an area of 400 square feet. If we view the real building as a dilation of the toy, what is the scale factor?

Answer 1

The scale factor is the ratio of the corresponding side lengths of the real building and the toy building. Since the area of the front side of the toy building is 1 square foot and the area of the front side of the real building is 400 square feet, the ratio of the areas is:

400/1 = 400

This tells us that the area of the real building is 400 times greater than the area of the toy building. Since area is a two-dimensional measure, we need to take the square root of this ratio to find the scale factor for the linear dimensions. Thus, the scale factor is:

sqrt(400) = 20

Therefore, the real building is 20 times larger than the toy building in terms of its linear dimensions.

Answer 2

The scale factor is 20.

Step-by-step explanation:

The scale factor is the ratio of the corresponding side lengths (or areas or volumes) of the two similar figures. In this case, we are given the areas of the front sides of the toy building and the real building, and we want to find the scale factor between them.

Let x be the scale factor. Then, the area of the front side of the real building is x^2 times the area of the front side of the toy building. We can set up the equation:

x^2 * 1 square foot = 400 square feet

Solving for x, we get:

x^2 = 400

x = sqrt(400)

x = 20

Therefore, the scale factor between the toy building and the real building is 20.