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A rectangular school banner has a length of 48 inches and a width of 30 inches. A sign is made that is similar to the school banner and has a length of 15 inches. What is the ratio of the area of the school banner to the area of the sign?

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barnuts

The ratio of length to width is:

ratio = 48 inches / 30 inches = 1.6

 

This ratio must be similar to that of the other school banner, therefore the width of that is:

width = 15 / 1.6 = 9.375 inches

 

The areas are:

A1 = 48 inches * 30 inches = 1440 square inches

A2 = 15 inches * 9.375 inches = 140.625 square inches

 

So the ratio of the area is:

A1 / A2 = 1440 / 140.625

A1 / A2 = 10.24

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