Constructing a scale model

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Question from Colleen, a student:

What is the formula i need to use to find out how to state a reasonable scale in the question below;
Suppose you were constructing a model that must sit on a piece of cardboard that is 22cm by 28cm. STATE THE REASONABLE SCALE that you can use to build a model to represent the following items. Determine the dimensions of the model.

a) a rectangular prism with a length of 5m and a width of 2m?

Colleen,

The prism is 5 m by 2 m so it's two and a half times as long as it is wide. The cardboard is closer to a square, 22 cm by 28 cm so if you scale the model so that the length fits within 28 cm then the width will easily fit in 22 cm. Hence you can ignore the width and focus on the length.

Lets put both lengths in the same units. Centimeters seems the most reasonable so the prism is 500 cm long an the model can't be more that 28 cm long. Just to make the arithmetic simple let's make the model 25 cm long. 500/25 = 20 so if the model is one-twentieth the size of the prism it will easily fit on the cardboard. (Check the width.) Now you have a decision to make. The model could be 3 cm longer so do you modify the scale factor to make the model larger and still fit or do you leave it at 20 so that the arithmetic is easy?

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.