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Let the dimensions be x and y:-

Perimeter: 2(x+y) = 24 => x+y = 12 => y = 12-x

Area: xy = 32 => x(12-x) = 32 => 12x-x2-32 = 0

Solving the above quadratic equation gives x = 4 and x = 8

Therfore the dimensions of the rectangle are 4 units by 8 units

Check: 2(4+8) = 24 units and 4*8 = 32 square units

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