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I have posted a link there to this topic so the OP can see my work.CALCULUS worded problems HELP?

5) Find the dimensions of the largest rectangle that can be inscribed in the ellipse 9x² + 16y² = 144. The sides of the rectangle are parallel to the axes of the ellipse.

6) An isosceles trapezoid has a lower base of 16 cm and the sloping sides are each 8 cm. Find the width of the upper base for greatest area.

7) A trapezoidal gutter is to be made from a sheet of tin 22 cm wide by bending up the edges. If the base is 14 cm wide, what width across the top gives the greatest carrying capacity?

Please EXPLAIN if necessary.