ratio of areas of 2 similar polygons is 16:25. If the perimeter of the first polygon is 200cm what is the perimeter of the second polygon.

Question

ratio of areas of 2 similar polygons is 16:25.  If the perimeter of the first polygon is 200cm what is the perimeter of the second polygon.

anonymous · Answer

The ratio of the areas of two similar polygons is the square of the ratio of their sides and their perimeter.
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In the picture, the ratio of sides from the smaller square to the bigger one is 2:4 or 1:2, but the ratio of their areas is 1:4, the square of that.

anonymous · Answer

What this means is that 16:25 is the square of the ratio of their perimeters. 16:25 is the square of 4:5, so thus the ratio of the perimeters is 4:5.
Now the first polygon is the smaller one, right?
Assuming it is, its perimeter is 200 cm: 4cm : 5cm  = 200cm : 250cm.
Therefore the perimeter of the second (larger?) polygon is 250cm.

Does that help? Was that too confusing?

anonymous · Answer

It is confusing, but I went through it slowly and you did a good job of explaining it.  I understand it.  thanks