Question 849366: Given that triangle ABC is similar to triangle FED,where AB = 77,EF = 21, BC = 11x + 11, and DE = 30.Find x.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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