Answer and Step-by-step explanation:
[tex]Greetings![/tex]
[tex]Let's~answer~your~question![/tex]
[tex]Since~ we~ know~ that ~these ~two~ are~ similar, ~it ~is ~also~ given ~that~ corresponding\\ parts ~of ~the~ triangle~ are ~proportional.~ In ~result,~ you~ can~ set~ the~ proportions~\\something~ like~ this:[/tex]
[tex]\frac{16}{32}= \frac{12}{24}[/tex]
[tex]Now,~from~ here, you~ can ~figure~ out~ that~ the~ ratio~ of ~the ~larger ~triangle~ to ~the \\~smaller~ triangle~ is ~.75:1[/tex]
[tex]You~can~ then~ apply~ this~ to~ the~ side ~of ~x-1 ~and ~set~ up ~the~ equation.[/tex]
[tex].75(x-1)=6[/tex]
[tex]Now,~solving~ the~ equation,~ you~ get~ x=9.~ Substitute~ that~ into~ x-1~ and~ you\\ get~ 8 ~as ~that~ side~ length.~ To~ check, compare:[/tex]
[tex]\frac{8}{6}=\frac{32}{24}[/tex]
[tex]Thus,~the~value~of~x~is=9.[/tex]
[tex]Hope~my~answer~helps~you!~Have~a~blessed~day~ahead![/tex]
[tex]-Isabelle~Williams[/tex]
