Answer:
5
Step-by-step explanation:
from the attached diagram, we can see that
LN = MP
3x + 1 = 8x -4
8x-3x = 1 + 4
5x = 5
x = 1
hence
LN = 3x+ 1 = 3(1) + 1 = 4
NM = 4x-1 = 4(1) - 1= 3
hence by Pythagorean formula,
diagonal NP = diagonal LM = √( 3² + 4²) = √25 = 5
