Answer:
[tex]d_2=6.43m[/tex]
Step-by-step explanation:
From the question we are told that:
Height of streetlight h_s=12
Height of Fatima H_f=5
Distance of streetlight from fatima d_1=9
Generally the equation for Synonymous is mathematically given by
 [tex]\frac{x'}{y'}=\frac{x}{y}[/tex]
Since
Triangle between Fatima's height and the streetlight  is synonymous with Fatima's height and her shadow
Therefore
 [tex]\frac{h'}{d_1}=\frac{h}{d_2}[/tex]
 [tex]\frac{12-5}{9}=\frac{5}{d_2}[/tex]
 [tex]d_2=6.43m[/tex]
Therefore
Her shadow is
 [tex]d_2=6.43m[/tex]
