A cuboid has length l cm, breadth b cm and height h cm.
a. (i) Draw and name a straight line segment representing the diagonal of the base of the cuboid. Write its length in terms of l and b.
b. (ii) Treating that diagonal and the height h as perpendicular sides of a right triangle inside the cuboid, obtain a simplified algebraic expression for the longest straight line segment that can be drawn within the cuboid.
c. (iii) Justify, with reference to the geometry of the cuboid, why the two right triangles used in (i) and (ii) exist.