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This question has a part A and B. Here is the question part A

 

 

This is Question part B

 

 Oct 17, 2018
 #1
avatar+98091 
+1

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

 

 

cool cool cool

 Oct 17, 2018
 #2
avatar+98091 
+1

Second one.....

 

Using the first answer...we know that

 

CA / BD  = 48/27

CA /36 = 48/27

CA/36 = 16/9

CA =  16 * 36 / 9

CA = 16 * 4

CA  = 64

 

 

cool cool cool

 Oct 17, 2018
 #3
avatar+464 
0

Thank you so much Chris

 Oct 18, 2018

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