Answer:
x = 4
Step-by-step explanation:
ΔLMN and ΔPMQ are similar. Therefore thw sides are in proportion:
[tex]\dfrac{LM}{PM}=\dfrac{NM}{QM}[/tex]
We have:
LM = 3 + 9 = 12
PM = 9
NM = x + 12
QM = 12
Substitute:
[tex]\dfrac{12}{9}=\dfrac{x+12}{12}[/tex] cross multiply
[tex]9(x+12)=(12)(12)[/tex]
[tex]9(x+12)=144[/tex] divide both sides by 9
[tex]\dfrac{9(x+12)}{9}=\dfrac{144}{9}[/tex]
[tex]x+12=16[/tex] subtract 12 from both sides
[tex]x=4[/tex]
