Express the perimeter P of a square as a function of the area.

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We need write the area of a square as a function of the perimeter.

Let us write the equation of the perimeter.

Let the side of a square be x.

Then the perimeter P = 4x.

==> x = P/4

Now we will write the equation of the area.

==> A = x^2

Now we will substitute with (1).

==> A = (P/4)^2 = p^2 /16

==> A(p) = p^2/ 16.

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