This question has a part A and B. Here is the question part A
This is Question part B
Here's the first one.....
angle EDB = angle CBA
Therefore.....
ΔCAB similar to ΔBED similar to ΔABD
BE = BD
CA = CB
AB = AD = 48
CA / AB = BE / ED CA / AB = AB / BD
CA /AB = BE / 27 CA / AD = AD / BD
CA /48 = BE / 27 CA * BD = AD^2
CA / BE = 48 / 27 CA * BD = 48^2
CA / BD = 48/27 CA = 48^2 / BD
Therefore
CA / BD = 48/27
(48^2 / BD) / BD = 48/27
48^2/ BD^2 = 48/27
48 / BD^2 = 1/27
48 * 27 = BD^2
1296 = BD^2
36 = BD