In parallelogram MNOP, PK=5x andKN=x2−14 .
What is PN?
Since PK and KN are opposite sides of a parallelogram, they must be equal in length.
Therefore, we have:
PK = KN
5x = x^2 - 14
Rearranging this equation, we get:
x^2 - 5x - 14 = 0
This quadratic equation can be factored as:
(x - 7)(x + 2) = 0
Setting each factor equal to zero, we have:
x - 7 = 0 or x + 2 = 0
x = 7 or x = -2
Since lengths cannot be negative, we discard x = -2.
Therefore, x = 7.
Now that we know the value of x, we can substitute it into the equation for PK:
PK = 5x = 5(7) = 35.
So, PN is also equal to 35.
Therefore, PN = 35.