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You are being asked to 'minimize' perimeter. Did you recognize that this is an optimization problem?
The first thing you will do is build a geometric equation that represents the situation. Then you will apply Calculus.

What do we know?

Now that we have an equation, P(h), let's find it's minimum value.

P '(h) = ___________________

To find the h-value of the max and min, set P ' (h) = 0, and solve for h.
Then, for a complete answer, don't forget to find the corresponding value of b.