Question

Yeah, I’ve tried to do this problem and still have no clue can anyone help me out maybe? And maybe explain how you got your answer too, so I can get it

Answer 1

Your answer is 70.

As this is a parallelogram, lines PN and MO are the same length. This also means K is the midpoint of line PN. From this, you can deduce that PK = KN as both are half of line PN

So, equating the expressions gives

$5x = {x}^{2} - 14$

And now we have to rearrange and solve for x by factorising

${x}^{2} - 5x - 14 = 0 \\ (x - 7)(x + 2) = 0 \\ x = 7 \\ x = - 2$

Now, if we substitute both values into PK =5x, we know that x cannot be - 2, as we cannot have a negative length.

Using x = 7 and substituting

$x = 7 \\ 5x = 35$

Then multiplying by 2 to give the entire length of PN

$10x = 70$