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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?
Your answer

User Roggie
by
6.8k points

2 Answers

12 votes

Final answer:

The scale factor between the real building and the toy building is 400.

Step-by-step explanation:

To find the scale factor, we need to compare the area of the real building's front side with the area of the toy building's front side.

The area of the real building's front side is 400 square feet and the area of the toy building's front side is 1 square foot.

To find the scale factor, we divide the area of the real building by the area of the toy building:

Scale factor = Area of Real Building / Area of Toy Building

Scale factor = 400 square feet / 1 square foot = 400

Therefore, the scale factor is 400, meaning that the real building is 400 times larger than the toy building.

User Muhwu
by
7.3k points
2 votes

Answer:


20

Step-by-step explanation:

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

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

So


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

Area scale factor is given by
k^2, where
k is the scale factor of the sides.

So,


(400)/(1)=k^2\\\Rightarrow k=√(400)\\\Rightarrow k=20

Hence, the scale factor is
20.

User Calley
by
7.3k points