Answer:
11
Step-by-step explanation:
To find LM we need PM. We can use the Pythagorean Theorem:
- a^2+b^2=c^2
- PN^2+PM^2=MN^2
- 5^2+PM^2=11^2
- 25+PM^2=121
- PM^2=96
- PM=√96
Now using the Pythagorean Theorem, we can find LM:
- a^2+b^2=c^2
- LP^2+PM^2=LM^2
- 5^2+(√96)^2=LM^2
- 25+96=LM^2
- 121=LM^2
- 11=LM
Or you could have seen that triangle LPM is congruent to triangle NPM by SAS (5, 90º, and PM) so LM=NM=11.
