Show that the longest simple path from a node \(x\) in a red-black tree to a descendant leaf has length at most twice that of the shortest simple path from node \(x\) to a descendant leaf.

Red-black property 5 tells us that both these simple paths must contain the same number of black nodes. Red-black property 4 tells us that the longest possible simpe path must be an alternating path with one red node for each black node. Thus the longest simple path from node \(x\) to a descendant leaf is at most twice as long as the shortest simple path from node \(x\) to a desendant leaf.