Answer:
[tex]x=54.6[/tex]
Step-by-step explanation:
Because ΔABC is similar to ΔSTU, we know that their corresponding sides are proportional. Therefore, we know that [tex]\frac{AB}{AC}=\frac{SU}{ST}[/tex]. We are given that [tex]AB=x[/tex], [tex]AC=21[/tex], [tex]SU=13[/tex], and [tex]ST=5[/tex]. After substituting the given values into the proportion and solving for [tex]x[/tex], we get:
[tex]\frac{AB}{AC}=\frac{SU}{ST}[/tex]
[tex]\frac{x}{21} =\frac{13}{5}[/tex] (Substitute given values into the proportion)
[tex]5*x=13*21[/tex] (Cross-Products Property)
[tex]5x=273[/tex] (Simplify)
[tex]\frac{5x}{5}=\frac{273}{5}[/tex] (Divide both sides of the equation by [tex]5[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=54.6[/tex] (Simplify)
Hope this helps!
