SOLUTION: If the areas of two similar decagons are 625 sq. ft. and 100 sq. ft., what is the ratio of the perimeters of the decagons?

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Question 191270: If the areas of two similar decagons are 625 sq. ft. and 100 sq. ft., what is the ratio of the perimeters of the decagons?
Answer by Edwin McCravy(6935) About Me  (Show Source):
You can put this solution on YOUR website!

Notice that the fact that they tell us they're decagons 
has nothing at all to do with the problem.  They could be
triangles, circles, trapezoids, parallelograms, or any
shape.

If you are given:

two similar plane figures,
two corresponding areas on their surfaces, measuring A1 and A2
two corresponding lengths on their surfaces, measuring L1 and L2,

then

%28L1%29%5E2%2F%28L2%29%5E2=%28A1%29%2F%28A2%29

So A1 = 625 and A2 = 100. Plugging in:

%28L1%29%5E2%2F%28L2%29%5E2=%28625%29%2F%28100%29

%28L1%29%5E2%2F%28L2%29%5E2=%28625%29%2F%28100%29

Reduce the fraction on the right:

%28L2%29%5E2%2F%28L2%29%5E2=25%2F4

Take positive square roots of both sides:

sqrt%28%28L1%29%5E2%2F%28L2%29%5E2%29=sqrt%2825%2F4%29

%28L1%29%2F%28L2%29=5%2F2 

So the ratio of perimeters is 5 to 2.

Edwin