Mark is building a scale model of his car as shown in the diagram. The actual car has a height of 10 feet and the model has a height of 1 foot at the same place.

A. What is the actual length of the car? Show your work.
B. Mark has model wheels with a diameter of 6 inches. If the actual wheel radius is 2.25 feet, will they be in proportion with his model? Justify your answer.

Question

contestada

Respuesta :

sqdancefan sqdancefan · Answer 1 · 2022-02-16T05:05:45+01:00

Answer:

A. 12.5 ft

B. not in proportion (should be 2.5 ft, not 2.25 ft)

Step-by-step explanation:

A scale model is one in which all linear dimensions of the model have the same ratio to corresponding linear dimensions of the object being modeled.

Here, that relationship means ...

actual length/model length = actual height/model height

actual length/(1.25 ft) = (10 ft)/(1 ft)

actual length = (1.25 ft)(10/1) = 12.5 ft

__

If the actual wheel has the same scale, we will have ...

actual diameter/(6 inches) = (10 ft)/(1 ft)

actual diameter = (6 inches)(10/1) = 60 inches = 5 ft

actual radius = (5 ft)/2 = 2.5 ft . . . . . at the same model scale

Since the actual wheel radius is 2.25 feet, it is not in proportion to the rest of the model.