Solve the problem by following the procedure for solving an optimization problem.

a. An open-topped storage box with a square base has a capacity of 5 m³. The material for the sides cost $1.60/m2, while the material for the bottom costs $2.00/ m². Find the dimensions that will minimize the cost of making the box.

b. The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the triangle of maximum area.