Find the dimensions and area of the rectangle of maximum area that can be inscribed in the following figures.

a. A right triangle with a given hypotenuse length L 

b. An equilateral triangle with a given side length L

c. A right triangle with a given area A 

d. An arbitrary triangle with a given area A (The result applies to any triangle, but first consider triangles for which all the angles are less than or equal to 90°.)