Question

CDKM is a parallelogram,

DA
⊥
CK
, DK – CD = 7
CA = 6, AK = 15
Find: CD and DK

Answer 1

If I understand the question correctly, then we have 2 right triangles;
ΔDAC and ΔDAK. To make our lives easier, we denote CD as x, DK as x+7, and DA as y. Since CA=6 and AK=15, we use the Pythagorean Theorem:
ΔDAC; CA²+DA²=CD²= 6²+y²=x²
ΔDAK; CA²+AK²=DK²= 15²+y²=(x+7)²
Using these two equations, we find that CD equals 10 and DK equals 17.
Hope it helps!

Answer 2

We have this parallelogram shown in the picture (just ignore the letters). Let's DK (in the picture it is AC) with x and CD (in the picture it is AD) with x-7. Applying Pythagoras theorem, we can write that DA (in the problem, in the picture it is AE) is
`DA^(2) = (x-7)^(2) - 36 = x^(2) - 225`. Solving this equation, we find the value of x and it is 106/7. That's the value of DK. And CD=106/7-7=57/7