Among all pairs of numbers with a sum 57 find the pair whose product is maximum

We know that

comparing the problem with the geometry, the rectangle with the largest area (maximum product of two numbers) is the square.
therefore
The pair of numbers, for 57, is 57/2 or 28.5
so
28.5+28.5> 57
28.5*28.5> 812.25

the answer is
the pair is 28.5 and 28.5

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