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Let D represent the length of the diagonal and A the area.
Suppose the sides are L and B.
Then A = L*B
and by Pythagoras, D2 = L2 + B2
These two equations need to be solved as simultaneous equations to get the values of L and B.
One way is to use the following identities:
(L + B)2 = L2 + 2LB + B2 = D2 + 2A so that L + B = sqrt(D2 + 2A)
and
(L - B)2 = L2 - 2LB + B2 = D2 - 2A so that L - B = sqrt(D2 - 2A)
which then give
2L = sqrt(D2 + 2A) + sqrt(D2 - 2A)
and
2B = sqrt(D2 + 2A) - sqrt(D2 - 2A)
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