Math CentralQuandaries & Queries


Question from td, a parent:

Two regular hexagons have areas of 54 square root of 3 and 150 square root of 3, what is the ratio of their perimeters?

Hi there.

When dealing with flat objects, the ratios of area dimensions are the square of the linear dimensions on similar (scaled) objects.

For example, a circle whose diameter is 3 units has an area of 2.25π. A circle whose diameter is 12 would have an area 16 times as large (because 12/3 is 4 and 42 is 16).

Another example: Two maps of the same region are available at different scales. In the first map, a farmer's field is 100 millimeters squared. In the second map, the same field is 2500 millimeters squared. What is the ratio of their perimeters? Answer: sqrt(2500/100) = 5:1.

Hope this helps,
Stephen La Rocque.

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