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?
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boffeemadrid boffeemadrid · Answer 1 · 2021-02-06T17:39:10+01:00

Answer:

[tex]20[/tex]

Step-by-step explanation:

The area of the front side of the toy model is [tex]1\ \text{ft}^2[/tex]

The area of the real building's front side is [tex]400\ \text{ft}^2[/tex]

So

[tex]1\ \text{ft}^2[/tex] of the toy model is equivalent to [tex]400\ \text{ft}^2[/tex] of the real building.

Area scale factor is given by [tex]k^2[/tex], where [tex]k[/tex] is the scale factor of the sides.

So,

[tex]\dfrac{400}{1}=k^2\\\Rightarrow k=\sqrt{400}\\\Rightarrow k=20[/tex]

Hence, the scale factor is [tex]20[/tex].

andromache andromache · Answer 2 · 2022-02-15T12:34:14+01:00

The scale factor should be 20.

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.

Since 1 square foot should be equal to 400 square feet

So,

[tex]400\div 1 = k^2[/tex]

[tex]K = \sqrt{400}[/tex]

k = 20

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