Answer:
x = 20
Step-by-step explanation:
In similar polygons, all corresponding sides are proportional. The scale factor between AB and DE is the same as between AC and DF.
[tex]\frac{DE}{AB}=\frac{DF}{AC}\\\\\frac{4+x}{4}=\frac{36}{6}\\\\6(4+x)=4(36)\\24+6x=144\\6x=120\\x=20[/tex]
You can confirm that by plugging it back into the original equation:
[tex]\frac{4+x}{4}=\frac{36}{6}\\\\\frac{4+(20)}{4}=\frac{36}{6}\\\\\frac{24}{4}=\frac{36}{6}\\\\6=6[/tex]
