Question

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

Answer 1

Answer:

$|PN|=70$

Step-by-step 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.

$\Rightarrow x=7$

$|PN|=2|PK|$

$|PN|=2(5(7))$

$|PN|=70$