Question

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

Answer 1

`|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`