MATH SOLVE

4 months ago

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

Accepted Solution

A:

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

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