1. **State the problem:** Given rectangle ABCD with sides AB = 5 in, BC = 12 in, CD = 5 in, DA = 12 in, and diagonals AC and BD intersecting at E. 2. **Find BD:** In a rectangle, diagonals are equal in length. Since AC = 13 in, BD = 13 in. 3. **Find CD:** Given as 5 in. 4. **Find AC:** Given as 13 in. 5. **Find AE:** Since diagonals bisect each other in a rectangle, AE = EC = 6.5 in. **Summary:** - BD = 13 in - CD = 5 in - AC = 13 in - AE = 6.5 in All given lengths are consistent with the properties of a rectangle and its diagonals.