Prof is right. I don't think we need to know how to prove this, but it requires differentiation..
Area = l*w
d^2 = l^2+w^2
=>w = SQRT(d^2-l^2)
Hence A = l*(d^2-l^2)^1/2
To find the maxima of this fn, we ned to differentiate this eqn and set
dA/dl = 0
=> 2*l^2 = d^2
=> l = d/SQRT(2) & w = d/SQRT(2)
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