Question

In a parallelogram MNOP, PK=5x and KN =x(squared) -14

What is PN

Answer 1

PN = 70

Explanation:

using the property that the diagonals bisect each other, then

PK = PN

5x = x² - 14 ( rearrange into standard form )

x² - 5x - 14 = 0 ← in standard form

(x - 7)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 2 = 0 ⇒ x = - 2

but x > 0 ⇒ x = 7

PN = PK + KN = 5x + x² - 14 = (5 × 7) + 7² - 14 = 35 + 49 - 14 = 70