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In parallelogram MNOP PK = 5x and KN = x2-14 what is PN?

In parallelogram MNOP PK = 5x and KN = x2-14 what is PN?-example-1
User Dietrich
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1 Answer

3 votes

Answer:


|PN|=70

Explanation:

The diagonals of a parallelogram bisect each other.

This implies that;


|PK|=|KN|


5x=x^2-14

We group all terms on the right hand side to obtain;


0=x^2-5x-14


\Rightarrow x^2-5x-14=0

Factor;


\Rightarrow x^2-7x+2x-14=0


\Rightarrow x(x-7)+2(x-7)=0


\Rightarrow (x-7)(x+2)=0


\Rightarrow (x-7)=0,(x+2)=0


\Rightarrow x=7,x=-2

We discard the negative value.


\Rightarrow x=7


|PN|=2|PK|


|PN|=2(5(7))


|PN|=70

User Quinma
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