Math CentralQuandaries & Queries

Question from Kip:

The ratio of the corresponding apothems of two similar regular pentagons is 5:7 What is the ratio of their areas?

Hi Kip,

In my diagram the apothems are of length $A$ and $a$ where $A:a = 7:5.$ Notice also that triangles $PQR$ and $TUV$ are similar.


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