Question 849366
if the triangles are similar, then the sides are proportional.


this means that AB  / EF = BC / DE


AB= 77
EF = 21
BC = 11x + 11
DE = 30


ratio becomes:


77 / 21 = (11x + 11) / 30


multiply both sides of this equation by 30 and you get:


(77 * 30) / 21 = 11x + 11


simplify this to get:


110 = 11x + 11


subtract 11 from both sides of this equation to get:


99 = 11x


divide both sides of this equation by 11 to get:


9 = x


that's your answer.


11x + 11 is equal to 99 + 11 is equal to 110.


the ratio of:


77 / 21 = (11x + 11) / 30 becomes:


77 / 21 = 110 / 30


cross multiply to get 77 * 30 = 21 * 110


simplify to get 2310 = 2310, confirming the solution of x = 9 is good.