Answer:
B. 28
Step-by-step explanation:
If ΔABC ~ ΔDEC, then the corresponding sides are in proportion:
[tex]\dfrac{AC}{DC}=\dfrac{AB}{DE}[/tex]
We have:
[tex]AC=x\\DC=32-x\\AB=42\\DE=6[/tex]
Substitute:
[tex]\dfrac{x}{32-x}=\dfrac{42}{6}[/tex]
[tex]\dfrac{x}{32-x}=\dfrac{7}{1}[/tex] cross multiply
[tex](1)(x)=(32-x)(7)[/tex] use distributive property
[tex]x=(32)(7)+(-x)(7)[/tex]
[tex]x=224-7x[/tex] add 7x to both sides
[tex]8x=224[/tex] divide both sides by 8
[tex]x=28[/tex]
