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Given pentagon ABCDE ~ pentagon FGHJK. The area of pentagon ABCDE is 1134 m^2 and
the area of pentagon FGHJK is 504 m^2. If the length of FK is 60m, what is the length of AE?
(How do I solve this using concepts of SIMILAR POLYGONS?)
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Consider the ratio of areas. It is = 2.25.
The ratio of the areas is the square of the similarity coefficient : = 2.25.
Hence, the similarity coefficient is the square root of this value : k = = 1.5.
Thus the ratio of the corresponding linear elements of the pentagon ABCDE to those
of the pentagon FGHJK is 1.5.
In particular, since the length of FK is 60 meters, then the length of the corresponding side AE is
1.5 times of 60 m, i.e. 90 m.
Solved and thoroughly explained.