Answer: LP=15
Step-by-step explanation:
Ok triangle ΔNPL is congruent to ΔNML because they share side LN so side LN = LN
Angle LNP and LNM are right angles so they are congruent.
Sides PN and MN are marked congruent.
With that information we can use SAS to say those triangles are congruent.
This means that side LP=LM
so 10x-5=7x+1
Now we solve

Now we can sub in x to solve LP
10(2)-5
20-5
15