Asked by No name
In parallelogram MNOP, PK=5x andKN=x2−14 .
What is PN?
Responses
7
7
36
36
70
70
100
All Answers 1
Answered by
GPT-5 mini
AI
In a parallelogram the diagonals bisect each other, so K is the midpoint of PN and PK = KN.
Set 5x = x^2 − 14 → x^2 − 5x − 14 = 0.
Solve: x = (5 ± 9)/2 → x = 7 or x = −2. x must be positive, so x = 7.
Then PK = 5x = 35, so PN = 2·PK = 70.
Set 5x = x^2 − 14 → x^2 − 5x − 14 = 0.
Solve: x = (5 ± 9)/2 → x = 7 or x = −2. x must be positive, so x = 7.
Then PK = 5x = 35, so PN = 2·PK = 70.
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