Given: CDKM is a parallelogram,DA ⊥ CK , DK – CD = 7 CA = 6, AK = 15 Find: CD and DK

With the information given, the triangle CAD and KAD are both right angled triangle and they share the base AD. 

So we can form 2 equation and solve them simultaneously. 

(AD)²=(CD)²-(AC)²
(AD)² = (CD)² - 6²                ...........(i)

(AD)² = (DK)² - (AK)²
(AD)² = (DK)² - 15²          ..............(ii)

But DK - CD = 7. So, DK=7+CD
Now let CD=x
From the 2 equations above, 
(AD)²=x²-36           .......(i)
(AD)²=(7+x)²-225   .......(ii)

x²-36=49+14x+x²-225
14x=140
x=10

CD = 10.

DK = 7+CD
      = 7+10
      = 17