In parallelogram MNOP, PK=5x andKN=x2−14 .

Question

What is PN?

Answer 1

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.