Answer:
[tex]|PN|=70[/tex]
Step-by-step explanation:
The diagonals of a parallelogram bisect each other.
This implies that;
[tex]|PK|=|KN|[/tex]
[tex]5x=x^2-14[/tex]
We group all terms on the right hand side to obtain;
[tex]0=x^2-5x-14[/tex]
[tex]\Rightarrow x^2-5x-14=0[/tex]
Factor;
[tex]\Rightarrow x^2-7x+2x-14=0[/tex]
[tex]\Rightarrow x(x-7)+2(x-7)=0[/tex]
[tex]\Rightarrow (x-7)(x+2)=0[/tex]
[tex]\Rightarrow (x-7)=0,(x+2)=0[/tex]
[tex]\Rightarrow x=7,x=-2[/tex]
We discard the negative value.
[tex]\Rightarrow x=7[/tex]
[tex]|PN|=2|PK|[/tex]
[tex]|PN|=2(5(7))[/tex]
[tex]|PN|=70[/tex]
