Question

*100 points* What is the value of x in these polygons?

Answer 1

Answer and Step-by-step explanation:

$Greetings!$

$Let's~answer~your~question!$

$Since~ we~ know~ that ~these ~two~ are~ similar, ~it ~is ~also~ given ~that~ corresponding\\ parts ~of ~the~ triangle~ are ~proportional.~ In ~result,~ you~ can~ set~ the~ proportions~\\something~ like~ this:$

$\frac{16}{32}= \frac{12}{24}$

$Now,~from~ here, you~ can ~figure~ out~ that~ the~ ratio~ of ~the ~larger ~triangle~ to ~the \\~smaller~ triangle~ is ~.75:1$

$You~can~ then~ apply~ this~ to~ the~ side ~of ~x-1 ~and ~set~ up ~the~ equation.$

$.75(x-1)=6$

$Now,~solving~ the~ equation,~ you~ get~ x=9.~ Substitute~ that~ into~ x-1~ and~ you\\ get~ 8 ~as ~that~ side~ length.~ To~ check, compare:$

$\frac{8}{6}=\frac{32}{24}$

$Thus,~the~value~of~x~is=9.$

$Hope~my~answer~helps~you!~Have~a~blessed~day~ahead!$

$-Isabelle~Williams$

Answer 2

Answer:

$x = 9$

Step-by-step explanation:

Step 1:  Make an expression

$\frac{x-1}{16} = \frac{6}{12}$

Step 2:  Cross multiply

$\frac{x-1}{16} = \frac{6}{12}$

$12(x-1) = 6*16$

Step 3:  Distribute

$12(x-1) = 6*16$

$(12*x)+(12*-1) = 96$

$12x - 12 = 96$

Step 4:  Add 12 to both sides

$12x - 12 + 12 = 96 + 12$

$12x = 108$

Step 5:  Divide both sides by 12

$12x / 12 = 108 / 12$

$x = 9$

Answer:  $x = 9$