Answer: 14 units
===================================================
Step-by-step explanation:
Rule: The diagonals of any rectangle are the same length.
Because of that rule, we can say
NQ = PR
(NK) + (KQ) = (PK) + (PR)
(x+4) + (2y+5) = (2x+1) + (4y+3)
x+2y+9 = 2x+4y+4
x+2y-2x-4y = 4-9
-x-2y = -5
x+2y = 5
------------------
Rule: The diagonals of any rectangle cut each other in half (aka bisect each other)
So the pieces NK and KQ are the same length.
NK = KQ
x+4 = 2y+5
x = 2y+5-4
x = 2y+1
Plug this into the previous equation we found. Solve for y.
x+2y = 5
(2y+1) + 2y = 5
4y+1 = 5
4y = 5-1
4y = 4
y = 4/4
y = 1
Then use this to find x
x = 2y+1
x = 2*1+1
x = 3
---------------
We now have enough info to find the length of each segment.
- NK = x+4 = 3+4 = 7
- KQ = 2y+5 = 2*1+5 = 7
- NQ = NK+KQ = 7+7 = 14 which is the final answer
Furthermore,
- PK = 2x+1 = 2*3+1 = 7
- KR = 4y+3 = 4*1+3 = 7
- PR = PK+KR = 7+7 = 14
We get identical segment lengths, which helps confirm the correct answer.