Answer :

smmwaite
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

In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

What is Pythagoras theorem?

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.

The difference of the side DK and CD is,

[tex]DK - CD = 7\\DK=7+CD[/tex]

The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,

[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex]              ....1

Again by using the Pythagoras theorem

[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]

Put the value of (AD)², from equation 1 in the above equation as,

[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]

Put the value of DK in the above equation as,

[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]

Hence, the value of DK is,

[tex]DK=7+10DK=17[/tex]

Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

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