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You need to solve the two equations

P = perimeter

A = area

B = width

H = height

P = 2B + 2H

A = BH

H = A/B

P = 2B + 2A/B

P = (2B^2 + 2A)/B

2B^2 -PB +2A = 0

use quadratic formula

B = (P +/- SQRT(P^2-16A))/4

ONE ROOT IS B, the other is H

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