This is a famous sequence (series) that has many applications in nature, art, etc.
The first few terms are..... 0 , 1, 1, 2, 3, 5, 8, 13.....
Notice that, afer the first two given terms, each successive term is just the sum of the previous two...!!
Here's an excellent resource for a tremendous amount of info about the Fibonacci Series.....http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html#relprime
[ I re-reading now, as a matter of fact !!! ]
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If the sides of the perimeter are integers, 1 is the minimum side length of any particular side. So, 49 would have to be the length of the adjacent side.....
Note 1 + 49 + 1 + 49 = 100 = the perimeter
So... the minimum square area would be (1) (49) = 49 square units...
Here's a graph of the situation with some of the integer possibilities......https://www.desmos.com/calculator/ap3s1jlsnv
Notice that after x = 1, the values of x from 2 to 25 inclusive all produce greater areas....!!!
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