Answer:
PM = 14.4
Step-by-step explanation:
In triangle MLK, PN || LK
Therefore, by Basic Proportionality Theorem:
[tex] \frac {PM}{PL} =\frac{15}{10}[/tex]
[tex] \frac {PL}{PM} =\frac{10}{15}[/tex]
(By invertendo)
[tex] \frac {PL+ PM}{PM} =\frac{10+15}{15}[/tex]
(By componendo)
[tex] \frac {LM}{PM} =\frac{25}{15}[/tex]
[tex] \frac {24}{PM} =\frac{5}{3}[/tex]
[tex]PM= \frac {24\times 3}{5} [/tex]
[tex]PM= \frac {72}{5} [/tex]
[tex]PM= 14.4 [/tex]
