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Given: CDKM is a parallelogram,DA ⊥ CK , DK – CD = 7 CA = 6, AK = 15 Find: CD an...
5 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