Question

A video game company is designing a game based on professional race cars. Professional race cars have a length of 570 cm and a width of 180 cm. The company wants a scaled image of the race car to fit within a rectangle on the game screen with a length of 13 cm and a width of 4 cm.

​ Part A -Knowing that the maximum width of the rectangle is 4 cm, what scale factor would result in the largest possible race car width that fits in the rectangle?

​Part B -​The video game company wants the width of the car on the game screen to be no smaller than 3 cm. What scale factor would result in the smallest possible image of the race car that meets this additional specification?

Explain

Answer 1

A) 1/45

B) 1/60

Explanation:

Part A

The actual car has a length to width ratio of ...

length/width = (570 cm)/(180 cm) = 57/18 = 3 1/6

The rectangle on the screen has a length to width ratio of ...

length/width = (13 cm)/(4 cm) = 3 1/4

Relative to its width, the screen rectangle is longer than necessary for a model of the car. So, the scale factor will be determined by the width of the car relative to the width of the screen model.

For a model width of 4 cm, the scale factor is ...

model/life-size = (4 cm)/(180 cm) = 1/45

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Part B

For a model width of 3 cm, the scale factor is ...

model/life-size = (3 cm)/(180 cm) = 1/60