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:`

`(16)/(32)= (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:`

`(8)/(6)=(32)/(24)`

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

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

`-Isabelle~Williams`

Answer 2

`x = 9`

Explanation:

Step 1: Make an expression

`(x-1)/(16) = (6)/(12)`

Step 2: Cross multiply

`(x-1)/(16) = (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`