Let 'a', 'b' and 'c' represent the side of the right triangle.

The are of a right triangle is (1/2)ab that is:

(ab)/2 = 20

ab = 40

The perimeter is 32 means:

a + b + c = 32

a + b = 32 - c

(a + b)^2 = (32 - c)^2

a^2 + 2ab + b^2 = (32 - c)^2

Since c^2 = a^2 + b^2 we have:

2*40 + c^2 = (32 - c)^2

(32 - c)^2 - c^2 - 80 = 0

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click here to see the equation solved for c

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c = 14.75

The hypotenuse is 14.75.