Answer:
C.) 70
Step-by-step explanation:
The line PN is made up of PK and KN (PN = PK + KN). We also know that PK must equal KN (definition of a parallelogram). Therefore, you can set the value of both lines equal to each other, solve for x, then add them together to find PN.
PN = ?
PK = 5x
KN = n² - 14
PK = KN <----- Both lines must equal one another
5x = n² - 14 <----- Substitute values in
0 = n² - 5x - 14 <----- Subtract 5x from both sides
0 = (x - 7)(x + 2) <----- Factor
x = 7 x = -2 <----- Set both parentheses equal to 0
The value for "x" can be 7 and -2. However, it does not make sense to use a negative value in this situation. If we were to plug -2 into the equations, it would result in lines with a negative value. Therefore, "x" must be 7. Next, plug this value in for "x" to find the numerical value of PK and KN.
PK = 5x -----> 5(7) = 35
KN = n² - 14 -----> (7)² - 14 = 35
The fact that these are equal makes sense. Now, add these two numbers to find the value of the overall line.
PK + KN = PN
35 + 35 = 70
Therefore, C.) 70 is the value of PN.
