Question

In parallelogram MNOP, if PN = 5x + (x^2 - 14), where x represents a variable. KN = x^2 - 14, what is the value of PN?

A) 7
B) 36
C) 70
D) 100

Answer 1

By setting PN equal to KN and simplifying, we find that x = 0, which when substituted back into the expression for PN, erroneously gives us a negative value of -14. This suggests there may be an error in the question or the information given, as the possible answers are all positive.

Step-by-step explanation:

To find the value of PN in the parallelogram MNOP, we are given that PN = 5x + (x2 - 14) and KN = x2 - 14. Since KN is a part of the parallelogram, and parallelograms have opposite sides that are equal in length, we can determine that PN = KN.

This means that:

1. x2 - 14 = 5x + (x2 - 14)
2. Simplify the equation: 0 = 5x
3. Solve for x: x = 0

Now, substituting x = 0 back into the expression for PN:

PN = 5(0) + (02 - 14) = -14

Since the value obtained for PN is negative and the given options are all positive, there might be a typo in the question or in our interpretation. However, following the provided steps should lead to the correct value for PN once it's verified if KN indeed equals PN or if there was different information intended to be applied.