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| Math Central | Quandaries & Queries |
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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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